9x-10(x^2-x-6)=0

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Solution for 9x-10(x^2-x-6)=0 equation:


Simplifying
9x + -10(x2 + -1x + -6) = 0

Reorder the terms:
9x + -10(-6 + -1x + x2) = 0
9x + (-6 * -10 + -1x * -10 + x2 * -10) = 0
9x + (60 + 10x + -10x2) = 0

Reorder the terms:
60 + 9x + 10x + -10x2 = 0

Combine like terms: 9x + 10x = 19x
60 + 19x + -10x2 = 0

Solving
60 + 19x + -10x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
-6 + -1.9x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -1.9x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -1.9x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1.9x + x2 = 0 + 6
-1.9x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-1.9x + x2 = 6

The x term is -1.9x.  Take half its coefficient (-0.95).
Square it (0.9025) and add it to both sides.

Add '0.9025' to each side of the equation.
-1.9x + 0.9025 + x2 = 6 + 0.9025

Reorder the terms:
0.9025 + -1.9x + x2 = 6 + 0.9025

Combine like terms: 6 + 0.9025 = 6.9025
0.9025 + -1.9x + x2 = 6.9025

Factor a perfect square on the left side:
(x + -0.95)(x + -0.95) = 6.9025

Calculate the square root of the right side: 2.627260931

Break this problem into two subproblems by setting 
(x + -0.95) equal to 2.627260931 and -2.627260931.

Subproblem 1

x + -0.95 = 2.627260931 Simplifying x + -0.95 = 2.627260931 Reorder the terms: -0.95 + x = 2.627260931 Solving -0.95 + x = 2.627260931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.95' to each side of the equation. -0.95 + 0.95 + x = 2.627260931 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + x = 2.627260931 + 0.95 x = 2.627260931 + 0.95 Combine like terms: 2.627260931 + 0.95 = 3.577260931 x = 3.577260931 Simplifying x = 3.577260931

Subproblem 2

x + -0.95 = -2.627260931 Simplifying x + -0.95 = -2.627260931 Reorder the terms: -0.95 + x = -2.627260931 Solving -0.95 + x = -2.627260931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.95' to each side of the equation. -0.95 + 0.95 + x = -2.627260931 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + x = -2.627260931 + 0.95 x = -2.627260931 + 0.95 Combine like terms: -2.627260931 + 0.95 = -1.677260931 x = -1.677260931 Simplifying x = -1.677260931

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.577260931, -1.677260931}

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