4x^2=32x+45

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Solution for 4x^2=32x+45 equation:


Simplifying
4x2 = 32x + 45

Reorder the terms:
4x2 = 45 + 32x

Solving
4x2 = 45 + 32x

Solving for variable 'x'.

Reorder the terms:
-45 + -32x + 4x2 = 45 + 32x + -45 + -32x

Reorder the terms:
-45 + -32x + 4x2 = 45 + -45 + 32x + -32x

Combine like terms: 45 + -45 = 0
-45 + -32x + 4x2 = 0 + 32x + -32x
-45 + -32x + 4x2 = 32x + -32x

Combine like terms: 32x + -32x = 0
-45 + -32x + 4x2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-11.25 + -8x + x2 = 0

Move the constant term to the right:

Add '11.25' to each side of the equation.
-11.25 + -8x + 11.25 + x2 = 0 + 11.25

Reorder the terms:
-11.25 + 11.25 + -8x + x2 = 0 + 11.25

Combine like terms: -11.25 + 11.25 = 0.00
0.00 + -8x + x2 = 0 + 11.25
-8x + x2 = 0 + 11.25

Combine like terms: 0 + 11.25 = 11.25
-8x + x2 = 11.25

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 11.25 + 16

Reorder the terms:
16 + -8x + x2 = 11.25 + 16

Combine like terms: 11.25 + 16 = 27.25
16 + -8x + x2 = 27.25

Factor a perfect square on the left side:
(x + -4)(x + -4) = 27.25

Calculate the square root of the right side: 5.220153254

Break this problem into two subproblems by setting 
(x + -4) equal to 5.220153254 and -5.220153254.

Subproblem 1

x + -4 = 5.220153254 Simplifying x + -4 = 5.220153254 Reorder the terms: -4 + x = 5.220153254 Solving -4 + x = 5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 5.220153254 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.220153254 + 4 x = 5.220153254 + 4 Combine like terms: 5.220153254 + 4 = 9.220153254 x = 9.220153254 Simplifying x = 9.220153254

Subproblem 2

x + -4 = -5.220153254 Simplifying x + -4 = -5.220153254 Reorder the terms: -4 + x = -5.220153254 Solving -4 + x = -5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -5.220153254 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.220153254 + 4 x = -5.220153254 + 4 Combine like terms: -5.220153254 + 4 = -1.220153254 x = -1.220153254 Simplifying x = -1.220153254

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.220153254, -1.220153254}

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