Algebra

Solve the quadratic equation.

4x^2-8x+3=5

4x² - 8x +3 - 5 = 0
4x²- 8x - 2 = 0
2x²- 4x -1 = 0

this is as far as I got. I am stuck and do not know what to do next can some one please help?



divide by two:
x²- 2x -1/2 = 0
Now add 1.5 to each side to complete the square:
x²- 2x -1/2 +1.5 = +1.5
(x-1)2=1.5
subtract 1.5 from each side
(x-1)2 -1.5 = 0

Now you have a difference of squares (1.5 is sqrt (3/2) squared..)
[x-1-sqrt3/2][x-1+sqrt3/2] = 0

divide by two:
x²- 2x -1/2 = 0
Now add 1.5 to each side to complete the square:
x²- 2x -1/2 +1.5 = +1.5
(x-1)2=1.5
subtract 1.5 from each side
(x-1)2 -1.5 = 0

Now you have a difference of squares (1.5 is sqrt (3/2) squared..)
[x-1-sqrt3/2][x-1+sqrt3/2] = 0

the answer is 0

  1. 👍
  2. 👎
  3. 👁

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    Prove 3(x+1)(x+7)-(2x+5)² is never positive So, 3(x+1)(x+7)-(2x+5)(2x+5) =3(x²+8x+7)-(4x²+20x+25) =3x²+24x+21-4x²-20x-25 =-x²+4x-4

  2. Math

    Use the simplex meth to solve the linear programming problem Maximize z = 8x1 + 2x2 Subject to: 4x1 + 3x2 < 11 X1 + 4x2 < 7 With x1 > 0, x2> 0

  3. pre cal

    Factor completely: 3x^2(4x2 + 1)^8 + 64x^4(4x2 + 1)^7.

  4. calculus

    An equation of the line tangent to the graph of f(x) = (4x2 - 8x + 3)4 at the point where x = 1 is:

  1. algebra

    What is the discriminant of the polynomial below? 4x2 + 4x + 1 A. 0 B. -4 C. -12 D. 32

  2. calculus

    Consider the function below. f(x) = 4x2 - 5x (a) Find f '(2). (b) Use the answer in part (a) to find an equation of the tangent line to the parabola y = 4x2 - 5x at the point (2, 6). y =

  3. Algebra

    Which of the following rewrites shows the correct process for completing the​ square? A- 4x2+9x+5=0 rewritten as 4x2+9x+814=−5+814 B- 3x2−6x−4=0 rewritten as x2−2x+1=4+1 C- 4x2+12x+7=0 rewritten as x2+3x+94=−74+94 D-

  4. Algebra

    What are the solutions of the quadratic equation below? 4x2 - 30x + 45 = 0

  1. Pre cal

    Fine a third degree polynomial function f(x) with real coefficients that has 4 and 2i are zeros and such that f(-1) =-50 4 21 -2i (x-4)(x-2i)(x+2i) (x-4)(x2+4) x3-16+4x-4x2 (x3-4x2+4x-16) -50=a(-1-4-4-16) -50=.25 a=2 Not

  2. Calculus

    Which of the following is the general solution of the differential equation dy/dx = 2x/y? y2 = x2 + C y2 = 2x2 + C

  3. Algebra 2

    Operations with Complex Numbers Simplify. 1. sqrt(-144) 2. sqrt(-64x^4) 3. sqrt(-13)*sqrt(-26) 4. (-2i)(-6i)(4i) 5. i13 6. i38 7. (5 – 2i) + (4 + 4i) 8. (3 – 4i) – (1 – 4i) 9. (3 + 4i)(3 – 4i) 10. (6 – 2i)(1 + i) 11.

  4. Algebra

    Please help.! 1) Given the following three points, find by hand the quadratic function they represent. (0,6), (2,16), (3, 33) A. f(x)=4x2−3x+6 B. f(x)=4x2+3x+6 C. f(x)=−4x2−3x+6 D. f(x)=−4x2+21x+6 2) Given the following

You can view more similar questions or ask a new question.