25x^2-30x-26=0

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Solution for 25x^2-30x-26=0 equation:


Simplifying
25x2 + -30x + -26 = 0

Reorder the terms:
-26 + -30x + 25x2 = 0

Solving
-26 + -30x + 25x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
25 the coefficient of the squared term: 

Divide each side by '25'.
-1.04 + -1.2x + x2 = 0

Move the constant term to the right:

Add '1.04' to each side of the equation.
-1.04 + -1.2x + 1.04 + x2 = 0 + 1.04

Reorder the terms:
-1.04 + 1.04 + -1.2x + x2 = 0 + 1.04

Combine like terms: -1.04 + 1.04 = 0.00
0.00 + -1.2x + x2 = 0 + 1.04
-1.2x + x2 = 0 + 1.04

Combine like terms: 0 + 1.04 = 1.04
-1.2x + x2 = 1.04

The x term is -1.2x.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2x + 0.36 + x2 = 1.04 + 0.36

Reorder the terms:
0.36 + -1.2x + x2 = 1.04 + 0.36

Combine like terms: 1.04 + 0.36 = 1.4
0.36 + -1.2x + x2 = 1.4

Factor a perfect square on the left side:
(x + -0.6)(x + -0.6) = 1.4

Calculate the square root of the right side: 1.183215957

Break this problem into two subproblems by setting 
(x + -0.6) equal to 1.183215957 and -1.183215957.

Subproblem 1

x + -0.6 = 1.183215957 Simplifying x + -0.6 = 1.183215957 Reorder the terms: -0.6 + x = 1.183215957 Solving -0.6 + x = 1.183215957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 1.183215957 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 1.183215957 + 0.6 x = 1.183215957 + 0.6 Combine like terms: 1.183215957 + 0.6 = 1.783215957 x = 1.783215957 Simplifying x = 1.783215957

Subproblem 2

x + -0.6 = -1.183215957 Simplifying x + -0.6 = -1.183215957 Reorder the terms: -0.6 + x = -1.183215957 Solving -0.6 + x = -1.183215957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -1.183215957 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -1.183215957 + 0.6 x = -1.183215957 + 0.6 Combine like terms: -1.183215957 + 0.6 = -0.583215957 x = -0.583215957 Simplifying x = -0.583215957

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.783215957, -0.583215957}

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