32x^2+64x+7=0

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Solution for 32x^2+64x+7=0 equation:


Simplifying
32x2 + 64x + 7 = 0

Reorder the terms:
7 + 64x + 32x2 = 0

Solving
7 + 64x + 32x2 = 0

Solving for variable 'x'.

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

Divide each side by '32'.
0.21875 + 2x + x2 = 0

Move the constant term to the right:

Add '-0.21875' to each side of the equation.
0.21875 + 2x + -0.21875 + x2 = 0 + -0.21875

Reorder the terms:
0.21875 + -0.21875 + 2x + x2 = 0 + -0.21875

Combine like terms: 0.21875 + -0.21875 = 0.00000
0.00000 + 2x + x2 = 0 + -0.21875
2x + x2 = 0 + -0.21875

Combine like terms: 0 + -0.21875 = -0.21875
2x + x2 = -0.21875

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -0.21875 + 1

Reorder the terms:
1 + 2x + x2 = -0.21875 + 1

Combine like terms: -0.21875 + 1 = 0.78125
1 + 2x + x2 = 0.78125

Factor a perfect square on the left side:
(x + 1)(x + 1) = 0.78125

Calculate the square root of the right side: 0.883883476

Break this problem into two subproblems by setting 
(x + 1) equal to 0.883883476 and -0.883883476.

Subproblem 1

x + 1 = 0.883883476 Simplifying x + 1 = 0.883883476 Reorder the terms: 1 + x = 0.883883476 Solving 1 + x = 0.883883476 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.883883476 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.883883476 + -1 x = 0.883883476 + -1 Combine like terms: 0.883883476 + -1 = -0.116116524 x = -0.116116524 Simplifying x = -0.116116524

Subproblem 2

x + 1 = -0.883883476 Simplifying x + 1 = -0.883883476 Reorder the terms: 1 + x = -0.883883476 Solving 1 + x = -0.883883476 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.883883476 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.883883476 + -1 x = -0.883883476 + -1 Combine like terms: -0.883883476 + -1 = -1.883883476 x = -1.883883476 Simplifying x = -1.883883476

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.116116524, -1.883883476}

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