# 9th grade algebra (completing square)

Can you check the following?
A1. (2x + 3)^2 = 25
sqrt(2x + 3)^2 = +-sqrt(25)
2x + 3 = +- 5
2x + 3 = 5, 2x + 3 = -5
2x = 2, 2x = -8
x = 1, x = -4
{-4, 1}

A2. x^2 + 14x + 45 = 0
x^2 + 14x + __ = -45 + __
x^2 + 14x + 49 = -45 + 49
(x +7)^2 = 4
sqrt(x+7)^2 = +- sqrt(4)
x + 7 = +- 2
x + 7 = 2, x +7 = -2
x = -5, x = -9
{-9, -5}

B2. 3x^2 + 12x - 1 = 14
3x^2 + 12x + __ = 14 + 1
3(x^2 + 4x + __) = 15 + __
3(x^2 + 4x + 4) = 15 + 12
3(x + 2)^2 = 27
(x + 2)^2 = 9
sqrt(x+2)^2 = +- sqrt(9)
x + 2 = +- 3
x + 2 = 3, x + 2 = -3
x = 1, x = -5
{-5, 1}

C1. 3x^2 - 12x - 66 = -3
3x^2 - 12x + __ = -3 + 66
3x^2 - 12x + __ = 63
3(x^2 - 4x + 4) = 63 + 12
3(x - 2)^2 = 75
(x - 2)^2 = 25
sqrt(x-2)^2 = +- sqrt(25)
x - 2 = +- 5
x - 2 = 5, x - 2 = -5
x = 7, x = -3
{-3, 7}

D1. 2x^2 - 12x - 11 = 3
2x^2 - 12x + __ = 3 + 11
2x^2 - 12x + __ = 14 + __
2(x^2 - 6x + 9) = 14 + 18
2(x-3)^2 = 32
(x-3)^2 = 16
sqrt(x-3)2 = +- sqrt(16)
x - 3 = +- 4
x - 3 = 4, x - 3 = -4
x = 7, x = -1
{-1, 7}

D2. (x+4)^2 = 49
sqrt(x+4)^2 = +- sqrt(49)
x + 4 = +- 7
x + 4 = 7, x + 4 = -7
x = 3, x = -11
{-11, 3}

E1. 4x^2 + 16x + 11 = 4
4x^2 + 16x + __ = 4 - 11
4x^2 + 16x + __ = -7 + __
4(x^2 + 4x + 4) = -7 + 16
4(x+2)^2 = 9
(x+2)^2 = 9/4
sqrt(x+2)^2 = +- sqrt(9/4)
x + 2 = +- 3/2
x + 2 = 3/2, x + 2 = -3/2
x = -1/2, x = -7/2
{-7/2, -1/2}

E2. x^2 - 16x = -63
(x^2 - 16x + 64) = -63 + 64
(x - 8)^2 = 1
sqrt(x - 8)^2 = +- sqrt(1)
x - 8 = +- 1
x - 8 = 1, x - 8 = -1
x = 9, x = 7
{7,9}

F2. x^2 + 8x - 63 = 21
x^2 + 8x + __ = 21 + 63
x^2 + 8x + 16 = 84 + 16
(x + 4)^2 = 100
sqrt(x + 4)^2 = +- sqrt(100)
x + 4 = 10, x + 4 = -10
x = 6, x = -14
{-14, 6}

G1. (4x - 1)^2 = 81
sqrt(4x-1)^2 = +- sqrt(81)
4x - 1 = +- 9
4x - 1 = 9, 4x -1 = -9
4x = 10 , 4x = -8
x = 10/4 , 4x = -2
x = 5/2
{-2, 5/2}

G2. x^2 + 10x + 13 = -3
x^2 + 10x + __ = -3 - 13
x^2 + 10x + 25 = -16 + 25
sqrt(x + 5)^2 = +- sqrt(9)
x + 5 = 3, x + 5 = -3
x = -2, x = -8
{-8, -2}

H1. x^2 - 2x + 3 = 27
x^2 - 2x + __ = 27 - 3
x^2 - 2x + 1 = 24 + 1
(x - 1)^2 = 25
sqrt(x - 1)^2 = +- sqrt(25)
x - 1 = +- 5
x - 1 = 5, x - 1 = -5
x = 6, x = -4
{-4, 6}

H2. 9x^2 - 18x - 18 = -2
9x^2 - 18x + __ = - 2 + 18 + __
9(x^2 - 2x + 1) = 16 + 9
9(x-1)^2 = 25
(x-1)^2 = 25/9
sqrt(x-1)^2 = +- sqrt(25/9)
x - 1 = +- 5/3
x - 1 = 5/3, x - 1 = -5/3
x = 8/3, x = -2/3
{-2/3, 8/3}

1. You seem to have a good grasp of doing these.
I verified most of your answers by subbing them back into the original equation.
All the ones I tried were correct.

posted by Reiny
2. Thanks for checking. For the ones above, they didn't match any anwers from the homework puzzle. So, I wasn't sure I was doing them correctly.

posted by Alexis

First Name

## Similar Questions

1. ### math,algebra,help

Directions are simplify by combining like terms. x radiacal 18 -3 radical 8x^2 can someone show me how to do these types of problems. thanks I cant determine the second term. For the first, I think you meant x sqrt(18) which
2. ### Algebra

Solve for s: h=(square root of 3)times s/2 and solve for h V= (pi)r squared h / 3 Solve for s: h=(square root of 3)times s/2 Multiply both sides by 2. 2h = (sqrt 3)*s*2/2 which cancels the 2 on the right. 2h = (sqrt 3)*s Now
3. ### Math

How do you find a square root of a number that's not a perfect square? I'm very confused. The book doesn't explain it too well. You can approximate it or simplify it in terms of (products of) square roots of smaller numbers. E.g.
4. ### algebra

can someone tell me if i did the problem correct (solve by completing the square) 4x^2+2x-3=0 x^2+(1/2)=3/4 x^2+(1/2)+(1/4)^2=3/4+(1/4)^2 (x+1/4)^2=13/16 x+1/4=+-sqrt 13/16 x+1/4=+-sqrt 13/4 x=-1/4+-sqrt 13/4 x=-1+-sqrt 13/4
5. ### math problem

I'm trying to get a handle on what square roots are (I think that's what they are called). Here is an example. 4(almost like a division sign but it is more like a check mark)3. I don't understand what it is, its a square root? and
6. ### math,help,algebra I

I need help can someone help me get unstuck and let me know if i am correct.thank you. solve by completing the square. 4x^2+2x-3=0 this is what i am doing: i used the quadratic equation. so where i am is in this step: x = (-2 (+-)
7. ### Math(Roots)

sqrt(24) *I don't really get this stuff.Can somebody please help me? The square root of 24 is 4.898979485566356 I know that..lol,but it says not to use decimals.Here is an example they gave me. Ex.sqrt(18)=sqrt(2*3*3)=3sqrt(2)