(5x^2+8x-64)=

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Solution for (5x^2+8x-64)= equation:


Simplifying
(5x2 + 8x + -64) = 0

Reorder the terms:
(-64 + 8x + 5x2) = 0

Remove parenthesis around (-64 + 8x + 5x2)
-64 + 8x + 5x2 = 0

Solving
-64 + 8x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-12.8 + 1.6x + x2 = 0

Move the constant term to the right:

Add '12.8' to each side of the equation.
-12.8 + 1.6x + 12.8 + x2 = 0 + 12.8

Reorder the terms:
-12.8 + 12.8 + 1.6x + x2 = 0 + 12.8

Combine like terms: -12.8 + 12.8 = 0.0
0.0 + 1.6x + x2 = 0 + 12.8
1.6x + x2 = 0 + 12.8

Combine like terms: 0 + 12.8 = 12.8
1.6x + x2 = 12.8

The x term is 1.6x.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6x + 0.64 + x2 = 12.8 + 0.64

Reorder the terms:
0.64 + 1.6x + x2 = 12.8 + 0.64

Combine like terms: 12.8 + 0.64 = 13.44
0.64 + 1.6x + x2 = 13.44

Factor a perfect square on the left side:
(x + 0.8)(x + 0.8) = 13.44

Calculate the square root of the right side: 3.666060556

Break this problem into two subproblems by setting 
(x + 0.8) equal to 3.666060556 and -3.666060556.

Subproblem 1

x + 0.8 = 3.666060556 Simplifying x + 0.8 = 3.666060556 Reorder the terms: 0.8 + x = 3.666060556 Solving 0.8 + x = 3.666060556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 3.666060556 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 3.666060556 + -0.8 x = 3.666060556 + -0.8 Combine like terms: 3.666060556 + -0.8 = 2.866060556 x = 2.866060556 Simplifying x = 2.866060556

Subproblem 2

x + 0.8 = -3.666060556 Simplifying x + 0.8 = -3.666060556 Reorder the terms: 0.8 + x = -3.666060556 Solving 0.8 + x = -3.666060556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -3.666060556 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -3.666060556 + -0.8 x = -3.666060556 + -0.8 Combine like terms: -3.666060556 + -0.8 = -4.466060556 x = -4.466060556 Simplifying x = -4.466060556

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.866060556, -4.466060556}

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