x^2-12.5x+34=0

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Solution for x^2-12.5x+34=0 equation:


Simplifying
x2 + -12.5x + 34 = 0

Reorder the terms:
34 + -12.5x + x2 = 0

Solving
34 + -12.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-34' to each side of the equation.
34 + -12.5x + -34 + x2 = 0 + -34

Reorder the terms:
34 + -34 + -12.5x + x2 = 0 + -34

Combine like terms: 34 + -34 = 0
0 + -12.5x + x2 = 0 + -34
-12.5x + x2 = 0 + -34

Combine like terms: 0 + -34 = -34
-12.5x + x2 = -34

The x term is -12.5x.  Take half its coefficient (-6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
-12.5x + 39.0625 + x2 = -34 + 39.0625

Reorder the terms:
39.0625 + -12.5x + x2 = -34 + 39.0625

Combine like terms: -34 + 39.0625 = 5.0625
39.0625 + -12.5x + x2 = 5.0625

Factor a perfect square on the left side:
(x + -6.25)(x + -6.25) = 5.0625

Calculate the square root of the right side: 2.25

Break this problem into two subproblems by setting 
(x + -6.25) equal to 2.25 and -2.25.

Subproblem 1

x + -6.25 = 2.25 Simplifying x + -6.25 = 2.25 Reorder the terms: -6.25 + x = 2.25 Solving -6.25 + x = 2.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 2.25 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 2.25 + 6.25 x = 2.25 + 6.25 Combine like terms: 2.25 + 6.25 = 8.5 x = 8.5 Simplifying x = 8.5

Subproblem 2

x + -6.25 = -2.25 Simplifying x + -6.25 = -2.25 Reorder the terms: -6.25 + x = -2.25 Solving -6.25 + x = -2.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -2.25 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -2.25 + 6.25 x = -2.25 + 6.25 Combine like terms: -2.25 + 6.25 = 4 x = 4 Simplifying x = 4

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.5, 4}

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