64=7x+x^2

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


Simplifying
64 = 7x + x2

Solving
64 = 7x + x2

Solving for variable 'x'.

Reorder the terms:
64 + -7x + -1x2 = 7x + -7x + x2 + -1x2

Combine like terms: 7x + -7x = 0
64 + -7x + -1x2 = 0 + x2 + -1x2
64 + -7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
64 + -7x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-64 + 7x + x2 = 0

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + 7x + 64 + x2 = 0 + 64

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

Combine like terms: -64 + 64 = 0
0 + 7x + x2 = 0 + 64
7x + x2 = 0 + 64

Combine like terms: 0 + 64 = 64
7x + x2 = 64

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 64 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 64 + 12.25

Combine like terms: 64 + 12.25 = 76.25
12.25 + 7x + x2 = 76.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 76.25

Calculate the square root of the right side: 8.732124598

Break this problem into two subproblems by setting 
(x + 3.5) equal to 8.732124598 and -8.732124598.

Subproblem 1

x + 3.5 = 8.732124598 Simplifying x + 3.5 = 8.732124598 Reorder the terms: 3.5 + x = 8.732124598 Solving 3.5 + x = 8.732124598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 8.732124598 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 8.732124598 + -3.5 x = 8.732124598 + -3.5 Combine like terms: 8.732124598 + -3.5 = 5.232124598 x = 5.232124598 Simplifying x = 5.232124598

Subproblem 2

x + 3.5 = -8.732124598 Simplifying x + 3.5 = -8.732124598 Reorder the terms: 3.5 + x = -8.732124598 Solving 3.5 + x = -8.732124598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -8.732124598 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -8.732124598 + -3.5 x = -8.732124598 + -3.5 Combine like terms: -8.732124598 + -3.5 = -12.232124598 x = -12.232124598 Simplifying x = -12.232124598

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.232124598, -12.232124598}

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