5x^2+52x+64=

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Solution for 5x^2+52x+64= equation:


Simplifying
5x2 + 52x + 64 = 0

Reorder the terms:
64 + 52x + 5x2 = 0

Solving
64 + 52x + 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 + 10.4x + x2 = 0

Move the constant term to the right:

Add '-12.8' to each side of the equation.
12.8 + 10.4x + -12.8 + x2 = 0 + -12.8

Reorder the terms:
12.8 + -12.8 + 10.4x + x2 = 0 + -12.8

Combine like terms: 12.8 + -12.8 = 0.0
0.0 + 10.4x + x2 = 0 + -12.8
10.4x + x2 = 0 + -12.8

Combine like terms: 0 + -12.8 = -12.8
10.4x + x2 = -12.8

The x term is 10.4x.  Take half its coefficient (5.2).
Square it (27.04) and add it to both sides.

Add '27.04' to each side of the equation.
10.4x + 27.04 + x2 = -12.8 + 27.04

Reorder the terms:
27.04 + 10.4x + x2 = -12.8 + 27.04

Combine like terms: -12.8 + 27.04 = 14.24
27.04 + 10.4x + x2 = 14.24

Factor a perfect square on the left side:
(x + 5.2)(x + 5.2) = 14.24

Calculate the square root of the right side: 3.773592453

Break this problem into two subproblems by setting 
(x + 5.2) equal to 3.773592453 and -3.773592453.

Subproblem 1

x + 5.2 = 3.773592453 Simplifying x + 5.2 = 3.773592453 Reorder the terms: 5.2 + x = 3.773592453 Solving 5.2 + x = 3.773592453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.2' to each side of the equation. 5.2 + -5.2 + x = 3.773592453 + -5.2 Combine like terms: 5.2 + -5.2 = 0.0 0.0 + x = 3.773592453 + -5.2 x = 3.773592453 + -5.2 Combine like terms: 3.773592453 + -5.2 = -1.426407547 x = -1.426407547 Simplifying x = -1.426407547

Subproblem 2

x + 5.2 = -3.773592453 Simplifying x + 5.2 = -3.773592453 Reorder the terms: 5.2 + x = -3.773592453 Solving 5.2 + x = -3.773592453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.2' to each side of the equation. 5.2 + -5.2 + x = -3.773592453 + -5.2 Combine like terms: 5.2 + -5.2 = 0.0 0.0 + x = -3.773592453 + -5.2 x = -3.773592453 + -5.2 Combine like terms: -3.773592453 + -5.2 = -8.973592453 x = -8.973592453 Simplifying x = -8.973592453

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.426407547, -8.973592453}

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