x^2-7x=61.25

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Solution for x^2-7x=61.25 equation:


Simplifying
x2 + -7x = 61.25

Reorder the terms:
-7x + x2 = 61.25

Solving
-7x + x2 = 61.25

Solving for variable 'x'.

Reorder the terms:
-61.25 + -7x + x2 = 61.25 + -61.25

Combine like terms: 61.25 + -61.25 = 0.00
-61.25 + -7x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '61.25' to each side of the equation.
-61.25 + -7x + 61.25 + x2 = 0.00 + 61.25

Reorder the terms:
-61.25 + 61.25 + -7x + x2 = 0.00 + 61.25

Combine like terms: -61.25 + 61.25 = 0.00
0.00 + -7x + x2 = 0.00 + 61.25
-7x + x2 = 0.00 + 61.25

Combine like terms: 0.00 + 61.25 = 61.25
-7x + x2 = 61.25

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 = 61.25 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 61.25 + 12.25

Combine like terms: 61.25 + 12.25 = 73.5
12.25 + -7x + x2 = 73.5

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 73.5

Calculate the square root of the right side: 8.5732141

Break this problem into two subproblems by setting 
(x + -3.5) equal to 8.5732141 and -8.5732141.

Subproblem 1

x + -3.5 = 8.5732141 Simplifying x + -3.5 = 8.5732141 Reorder the terms: -3.5 + x = 8.5732141 Solving -3.5 + x = 8.5732141 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 = 8.5732141 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 8.5732141 + 3.5 x = 8.5732141 + 3.5 Combine like terms: 8.5732141 + 3.5 = 12.0732141 x = 12.0732141 Simplifying x = 12.0732141

Subproblem 2

x + -3.5 = -8.5732141 Simplifying x + -3.5 = -8.5732141 Reorder the terms: -3.5 + x = -8.5732141 Solving -3.5 + x = -8.5732141 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 = -8.5732141 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -8.5732141 + 3.5 x = -8.5732141 + 3.5 Combine like terms: -8.5732141 + 3.5 = -5.0732141 x = -5.0732141 Simplifying x = -5.0732141

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.0732141, -5.0732141}

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