15x^2-8x-18=

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Solution for 15x^2-8x-18= equation:


Simplifying
15x2 + -8x + -18 = 0

Reorder the terms:
-18 + -8x + 15x2 = 0

Solving
-18 + -8x + 15x2 = 0

Solving for variable 'x'.

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

Divide each side by '15'.
-1.2 + -0.5333333333x + x2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + -0.5333333333x + 1.2 + x2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + -0.5333333333x + x2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + -0.5333333333x + x2 = 0 + 1.2
-0.5333333333x + x2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
-0.5333333333x + x2 = 1.2

The x term is -0.5333333333x.  Take half its coefficient (-0.2666666667).
Square it (0.07111111113) and add it to both sides.

Add '0.07111111113' to each side of the equation.
-0.5333333333x + 0.07111111113 + x2 = 1.2 + 0.07111111113

Reorder the terms:
0.07111111113 + -0.5333333333x + x2 = 1.2 + 0.07111111113

Combine like terms: 1.2 + 0.07111111113 = 1.27111111113
0.07111111113 + -0.5333333333x + x2 = 1.27111111113

Factor a perfect square on the left side:
(x + -0.2666666667)(x + -0.2666666667) = 1.27111111113

Calculate the square root of the right side: 1.127435635

Break this problem into two subproblems by setting 
(x + -0.2666666667) equal to 1.127435635 and -1.127435635.

Subproblem 1

x + -0.2666666667 = 1.127435635 Simplifying x + -0.2666666667 = 1.127435635 Reorder the terms: -0.2666666667 + x = 1.127435635 Solving -0.2666666667 + x = 1.127435635 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2666666667' to each side of the equation. -0.2666666667 + 0.2666666667 + x = 1.127435635 + 0.2666666667 Combine like terms: -0.2666666667 + 0.2666666667 = 0.0000000000 0.0000000000 + x = 1.127435635 + 0.2666666667 x = 1.127435635 + 0.2666666667 Combine like terms: 1.127435635 + 0.2666666667 = 1.3941023017 x = 1.3941023017 Simplifying x = 1.3941023017

Subproblem 2

x + -0.2666666667 = -1.127435635 Simplifying x + -0.2666666667 = -1.127435635 Reorder the terms: -0.2666666667 + x = -1.127435635 Solving -0.2666666667 + x = -1.127435635 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2666666667' to each side of the equation. -0.2666666667 + 0.2666666667 + x = -1.127435635 + 0.2666666667 Combine like terms: -0.2666666667 + 0.2666666667 = 0.0000000000 0.0000000000 + x = -1.127435635 + 0.2666666667 x = -1.127435635 + 0.2666666667 Combine like terms: -1.127435635 + 0.2666666667 = -0.8607689683 x = -0.8607689683 Simplifying x = -0.8607689683

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.3941023017, -0.8607689683}

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