x^2-7x=23.75

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Solution for x^2-7x=23.75 equation:


Simplifying
x2 + -7x = 23.75

Reorder the terms:
-7x + x2 = 23.75

Solving
-7x + x2 = 23.75

Solving for variable 'x'.

Reorder the terms:
-23.75 + -7x + x2 = 23.75 + -23.75

Combine like terms: 23.75 + -23.75 = 0.00
-23.75 + -7x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '23.75' to each side of the equation.
-23.75 + -7x + 23.75 + x2 = 0.00 + 23.75

Reorder the terms:
-23.75 + 23.75 + -7x + x2 = 0.00 + 23.75

Combine like terms: -23.75 + 23.75 = 0.00
0.00 + -7x + x2 = 0.00 + 23.75
-7x + x2 = 0.00 + 23.75

Combine like terms: 0.00 + 23.75 = 23.75
-7x + x2 = 23.75

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 = 23.75 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 23.75 + 12.25

Combine like terms: 23.75 + 12.25 = 36
12.25 + -7x + x2 = 36

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 36

Calculate the square root of the right side: 6

Break this problem into two subproblems by setting 
(x + -3.5) equal to 6 and -6.

Subproblem 1

x + -3.5 = 6 Simplifying x + -3.5 = 6 Reorder the terms: -3.5 + x = 6 Solving -3.5 + x = 6 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 = 6 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 6 + 3.5 x = 6 + 3.5 Combine like terms: 6 + 3.5 = 9.5 x = 9.5 Simplifying x = 9.5

Subproblem 2

x + -3.5 = -6 Simplifying x + -3.5 = -6 Reorder the terms: -3.5 + x = -6 Solving -3.5 + x = -6 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 = -6 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -6 + 3.5 x = -6 + 3.5 Combine like terms: -6 + 3.5 = -2.5 x = -2.5 Simplifying x = -2.5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.5, -2.5}

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