9x^2+4-14x-8x^2-15x=

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Solution for 9x^2+4-14x-8x^2-15x= equation:


Simplifying
9x2 + 4 + -14x + -8x2 + -15x = 0

Reorder the terms:
4 + -14x + -15x + 9x2 + -8x2 = 0

Combine like terms: -14x + -15x = -29x
4 + -29x + 9x2 + -8x2 = 0

Combine like terms: 9x2 + -8x2 = 1x2
4 + -29x + 1x2 = 0

Solving
4 + -29x + 1x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -29x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -29x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -29x + x2 = 0 + -4
-29x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-29x + x2 = -4

The x term is -29x.  Take half its coefficient (-14.5).
Square it (210.25) and add it to both sides.

Add '210.25' to each side of the equation.
-29x + 210.25 + x2 = -4 + 210.25

Reorder the terms:
210.25 + -29x + x2 = -4 + 210.25

Combine like terms: -4 + 210.25 = 206.25
210.25 + -29x + x2 = 206.25

Factor a perfect square on the left side:
(x + -14.5)(x + -14.5) = 206.25

Calculate the square root of the right side: 14.361406616

Break this problem into two subproblems by setting 
(x + -14.5) equal to 14.361406616 and -14.361406616.

Subproblem 1

x + -14.5 = 14.361406616 Simplifying x + -14.5 = 14.361406616 Reorder the terms: -14.5 + x = 14.361406616 Solving -14.5 + x = 14.361406616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = 14.361406616 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = 14.361406616 + 14.5 x = 14.361406616 + 14.5 Combine like terms: 14.361406616 + 14.5 = 28.861406616 x = 28.861406616 Simplifying x = 28.861406616

Subproblem 2

x + -14.5 = -14.361406616 Simplifying x + -14.5 = -14.361406616 Reorder the terms: -14.5 + x = -14.361406616 Solving -14.5 + x = -14.361406616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = -14.361406616 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = -14.361406616 + 14.5 x = -14.361406616 + 14.5 Combine like terms: -14.361406616 + 14.5 = 0.138593384 x = 0.138593384 Simplifying x = 0.138593384

Solution

The solution to the problem is based on the solutions from the subproblems. x = {28.861406616, 0.138593384}

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