7.5(7.5)=x(x+6.25)

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Solution for 7.5(7.5)=x(x+6.25) equation: 


Simplifying
7.5(7.5) = x(x + 6.25)

Multiply 7.5 * 7.5
56.25 = x(x + 6.25)

Reorder the terms:
56.25 = x(6.25 + x)
56.25 = (6.25 * x + x * x)
56.25 = (6.25x + x2)

Solving
56.25 = 6.25x + x2

Solving for variable 'x'.

Reorder the terms:
56.25 + -6.25x + -1x2 = 6.25x + -6.25x + x2 + -1x2

Combine like terms: 6.25x + -6.25x = 0.00
56.25 + -6.25x + -1x2 = 0.00 + x2 + -1x2
56.25 + -6.25x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
56.25 + -6.25x + -1x2 = 0

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

Divide each side by '-1'.
-56.25 + 6.25x + x2 = 0

Move the constant term to the right:

Add '56.25' to each side of the equation.
-56.25 + 6.25x + 56.25 + x2 = 0 + 56.25

Reorder the terms:
-56.25 + 56.25 + 6.25x + x2 = 0 + 56.25

Combine like terms: -56.25 + 56.25 = 0.00
0.00 + 6.25x + x2 = 0 + 56.25
6.25x + x2 = 0 + 56.25

Combine like terms: 0 + 56.25 = 56.25
6.25x + x2 = 56.25

The x term is 6.25x.  Take half its coefficient (3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
6.25x + 9.765625 + x2 = 56.25 + 9.765625

Reorder the terms:
9.765625 + 6.25x + x2 = 56.25 + 9.765625

Combine like terms: 56.25 + 9.765625 = 66.015625
9.765625 + 6.25x + x2 = 66.015625

Factor a perfect square on the left side:
(x + 3.125)(x + 3.125) = 66.015625

Calculate the square root of the right side: 8.125

Break this problem into two subproblems by setting 
(x + 3.125) equal to 8.125 and -8.125.


Subproblem 1
x + 3.125 = 8.125

Simplifying
x + 3.125 = 8.125

Reorder the terms:
3.125 + x = 8.125

Solving
3.125 + x = 8.125

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3.125' to each side of the equation.
3.125 + -3.125 + x = 8.125 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + x = 8.125 + -3.125
x = 8.125 + -3.125

Combine like terms: 8.125 + -3.125 = 5
x = 5

Simplifying
x = 5


Subproblem 2
x + 3.125 = -8.125

Simplifying
x + 3.125 = -8.125

Reorder the terms:
3.125 + x = -8.125

Solving
3.125 + x = -8.125

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3.125' to each side of the equation.
3.125 + -3.125 + x = -8.125 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + x = -8.125 + -3.125
x = -8.125 + -3.125

Combine like terms: -8.125 + -3.125 = -11.25
x = -11.25

Simplifying
x = -11.25


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5, -11.25}

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