x^2-2.5x+1.5625=7.5625

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Solution for x^2-2.5x+1.5625=7.5625 equation:


Simplifying
x2 + -2.5x + 1.5625 = 7.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 7.5625

Solving
1.5625 + -2.5x + x2 = 7.5625

Solving for variable 'x'.

Reorder the terms:
1.5625 + -7.5625 + -2.5x + x2 = 7.5625 + -7.5625

Combine like terms: 1.5625 + -7.5625 = -6
-6 + -2.5x + x2 = 7.5625 + -7.5625

Combine like terms: 7.5625 + -7.5625 = 0.0000
-6 + -2.5x + x2 = 0.0000

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -2.5x + 6 + x2 = 0.0000 + 6

Reorder the terms:
-6 + 6 + -2.5x + x2 = 0.0000 + 6

Combine like terms: -6 + 6 = 0
0 + -2.5x + x2 = 0.0000 + 6
-2.5x + x2 = 0.0000 + 6

Combine like terms: 0.0000 + 6 = 6
-2.5x + x2 = 6

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 6 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 6 + 1.5625

Combine like terms: 6 + 1.5625 = 7.5625
1.5625 + -2.5x + x2 = 7.5625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 7.5625

Calculate the square root of the right side: 2.75

Break this problem into two subproblems by setting 
(x + -1.25) equal to 2.75 and -2.75.

Subproblem 1

x + -1.25 = 2.75 Simplifying x + -1.25 = 2.75 Reorder the terms: -1.25 + x = 2.75 Solving -1.25 + x = 2.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 2.75 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.75 + 1.25 x = 2.75 + 1.25 Combine like terms: 2.75 + 1.25 = 4 x = 4 Simplifying x = 4

Subproblem 2

x + -1.25 = -2.75 Simplifying x + -1.25 = -2.75 Reorder the terms: -1.25 + x = -2.75 Solving -1.25 + x = -2.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -2.75 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.75 + 1.25 x = -2.75 + 1.25 Combine like terms: -2.75 + 1.25 = -1.5 x = -1.5 Simplifying x = -1.5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4, -1.5}

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