Solve for "x" in each equation.
1)xsquared+12x+25= 0
2)xsquared+4x-12= 0
3)xsquared-5x= 50
4)(x+1)squared= 169
5)2xsquared+5x= 12
6)(2x-5)squared= 225
7)x-4/x-3 = x+2/x+1
8)9/2x+1/3= 1/2
9)6/x-1= 3/x
10)2x/2x+2x= 4
You are obviously studying quadratic equations.
With what specific part of this assignment are you having difficulties ?
I will pick two at random
1. x^2 + 12x + 25 = 0
Since the quadratic term has a coefficent of 1 and the middle term is even, completing the square works best
x^2 + 12x = -25
x^2 + 12x + 36 = -25+36
(x+6)^2 = 11
x+6 = ± √11
x = -6 ± √11
for #7 , you must mean
(x-4)/(x-3) = (x+2)/(x+1)
cross-multiply ...
x^2 -3x - 4 = x^2 - x - 6
-2x = -2
x = 1
can you see why my brackets are essential ?
let me know what you get for the others.
To solve for "x" in each equation, we will follow different methods based on the type of equation. Here's how to solve each equation:
1) x^2 + 12x + 25 = 0:
This is a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:
(x + 5)(x + 5) = 0
(x + 5)^2 = 0
Now, we can take the square root of both sides:
x + 5 = 0
x = -5
2) x^2 + 4x - 12 = 0:
Similarly, this is a quadratic equation. Let's use factoring to solve it:
(x - 2)(x + 6) = 0
x - 2 = 0 or x + 6 = 0
x = 2 or x = -6
3) x^2 - 5x = 50:
Move all terms to one side to form a quadratic equation:
x^2 - 5x - 50 = 0
This equation can be factored as:
(x - 10)(x + 5) = 0
x - 10 = 0 or x + 5 = 0
x = 10 or x = -5
4) (x + 1)^2 = 169:
This is a quadratic equation with the square of a binomial. Take the square root of both sides:
x + 1 = ± √169
x + 1 = ± 13
x = -1 ± 13
x = -14 or x = 12
5) 2x^2 + 5x = 12:
Rearrange the equation to form a quadratic equation:
2x^2 + 5x - 12 = 0
Now, let's solve this quadratic equation using factoring:
(2x - 3)(x + 4) = 0
2x - 3 = 0 or x + 4 = 0
x = 3/2 or x = -4
6) (2x - 5)^2 = 225:
Take the square roots of both sides:
2x - 5 = ±√225
2x - 5 = ±15
x = (5 ± 15)/2
x = 10/2 or x = -10/2
x = 5 or x = -5
7) (x - 4)/(x - 3) = (x + 2)/(x + 1):
Cross-multiply to eliminate the fractions:
(x - 4)(x + 1) = (x - 3)(x + 2)
Now, expand and simplify both sides of the equation:
x^2 - 3x + x - 4 = x^2 + 2x - 3x - 6
Simplify the equation further:
x^2 - 2x - 4 = x^2 - x - 6
Move all terms to one side:
-2x - 4 + x + 6 = 0
Combine like terms:
-x + 2 = 0
Multiply both sides by -1 to eliminate the negative sign:
x - 2 = 0
x = 2
8) 9/(2x + 1) = 1/2:
Cross-multiply to eliminate the fractions:
9 * 2 = 1 * (2x + 1)
18 = 2x + 1
Simplify the equation:
2x = 18 - 1
2x = 17
Divide both sides by 2 to solve for x:
x = 17/2 or x = 8.5
9) 6/(x - 1) = 3/x:
Cross-multiply to eliminate the fractions:
6x = 3(x - 1)
Distribute on the right side:
6x = 3x - 3
Move all terms to one side:
6x - 3x = -3
Combine like terms:
3x = -3
Divide both sides by 3 to solve for x:
x = -3/3
x = -1
10) (2x)/(2x + 2x) = 4:
Combine like terms in the denominator:
(2x)/(4x) = 4
Divide both sides by (2x) to solve for x:
1/2 = 4
This equation has no solutions since the left side is less than the right side.