x^2-25x+17=-9x+10

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Solution for x^2-25x+17=-9x+10 equation:


Simplifying
x2 + -25x + 17 = -9x + 10

Reorder the terms:
17 + -25x + x2 = -9x + 10

Reorder the terms:
17 + -25x + x2 = 10 + -9x

Solving
17 + -25x + x2 = 10 + -9x

Solving for variable 'x'.

Reorder the terms:
17 + -10 + -25x + 9x + x2 = 10 + -9x + -10 + 9x

Combine like terms: 17 + -10 = 7
7 + -25x + 9x + x2 = 10 + -9x + -10 + 9x

Combine like terms: -25x + 9x = -16x
7 + -16x + x2 = 10 + -9x + -10 + 9x

Reorder the terms:
7 + -16x + x2 = 10 + -10 + -9x + 9x

Combine like terms: 10 + -10 = 0
7 + -16x + x2 = 0 + -9x + 9x
7 + -16x + x2 = -9x + 9x

Combine like terms: -9x + 9x = 0
7 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -16x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + -16x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -16x + x2 = 0 + -7
-16x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-16x + x2 = -7

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = -7 + 64

Reorder the terms:
64 + -16x + x2 = -7 + 64

Combine like terms: -7 + 64 = 57
64 + -16x + x2 = 57

Factor a perfect square on the left side:
(x + -8)(x + -8) = 57

Calculate the square root of the right side: 7.549834435

Break this problem into two subproblems by setting 
(x + -8) equal to 7.549834435 and -7.549834435.

Subproblem 1

x + -8 = 7.549834435 Simplifying x + -8 = 7.549834435 Reorder the terms: -8 + x = 7.549834435 Solving -8 + x = 7.549834435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 7.549834435 + 8 Combine like terms: -8 + 8 = 0 0 + x = 7.549834435 + 8 x = 7.549834435 + 8 Combine like terms: 7.549834435 + 8 = 15.549834435 x = 15.549834435 Simplifying x = 15.549834435

Subproblem 2

x + -8 = -7.549834435 Simplifying x + -8 = -7.549834435 Reorder the terms: -8 + x = -7.549834435 Solving -8 + x = -7.549834435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -7.549834435 + 8 Combine like terms: -8 + 8 = 0 0 + x = -7.549834435 + 8 x = -7.549834435 + 8 Combine like terms: -7.549834435 + 8 = 0.450165565 x = 0.450165565 Simplifying x = 0.450165565

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.549834435, 0.450165565}

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