=15x^2-8x-13

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Solution for =15x^2-8x-13 equation:


Simplifying
0 = 15x2 + -8x + -13

Reorder the terms:
0 = -13 + -8x + 15x2

Solving
0 = -13 + -8x + 15x2

Solving for variable 'x'.

Combine like terms: 0 + 13 = 13
13 + 8x + -15x2 = -13 + -8x + 15x2 + 13 + 8x + -15x2

Reorder the terms:
13 + 8x + -15x2 = -13 + 13 + -8x + 8x + 15x2 + -15x2

Combine like terms: -13 + 13 = 0
13 + 8x + -15x2 = 0 + -8x + 8x + 15x2 + -15x2
13 + 8x + -15x2 = -8x + 8x + 15x2 + -15x2

Combine like terms: -8x + 8x = 0
13 + 8x + -15x2 = 0 + 15x2 + -15x2
13 + 8x + -15x2 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
13 + 8x + -15x2 = 0

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

Divide each side by '-15'.
-0.8666666667 + -0.5333333333x + x2 = 0

Move the constant term to the right:

Add '0.8666666667' to each side of the equation.
-0.8666666667 + -0.5333333333x + 0.8666666667 + x2 = 0 + 0.8666666667

Reorder the terms:
-0.8666666667 + 0.8666666667 + -0.5333333333x + x2 = 0 + 0.8666666667

Combine like terms: -0.8666666667 + 0.8666666667 = 0.0000000000
0.0000000000 + -0.5333333333x + x2 = 0 + 0.8666666667
-0.5333333333x + x2 = 0 + 0.8666666667

Combine like terms: 0 + 0.8666666667 = 0.8666666667
-0.5333333333x + x2 = 0.8666666667

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 = 0.8666666667 + 0.07111111113

Reorder the terms:
0.07111111113 + -0.5333333333x + x2 = 0.8666666667 + 0.07111111113

Combine like terms: 0.8666666667 + 0.07111111113 = 0.93777777783
0.07111111113 + -0.5333333333x + x2 = 0.93777777783

Factor a perfect square on the left side:
(x + -0.2666666667)(x + -0.2666666667) = 0.93777777783

Calculate the square root of the right side: 0.96838927

Break this problem into two subproblems by setting 
(x + -0.2666666667) equal to 0.96838927 and -0.96838927.

Subproblem 1

x + -0.2666666667 = 0.96838927 Simplifying x + -0.2666666667 = 0.96838927 Reorder the terms: -0.2666666667 + x = 0.96838927 Solving -0.2666666667 + x = 0.96838927 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 = 0.96838927 + 0.2666666667 Combine like terms: -0.2666666667 + 0.2666666667 = 0.0000000000 0.0000000000 + x = 0.96838927 + 0.2666666667 x = 0.96838927 + 0.2666666667 Combine like terms: 0.96838927 + 0.2666666667 = 1.2350559367 x = 1.2350559367 Simplifying x = 1.2350559367

Subproblem 2

x + -0.2666666667 = -0.96838927 Simplifying x + -0.2666666667 = -0.96838927 Reorder the terms: -0.2666666667 + x = -0.96838927 Solving -0.2666666667 + x = -0.96838927 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 = -0.96838927 + 0.2666666667 Combine like terms: -0.2666666667 + 0.2666666667 = 0.0000000000 0.0000000000 + x = -0.96838927 + 0.2666666667 x = -0.96838927 + 0.2666666667 Combine like terms: -0.96838927 + 0.2666666667 = -0.7017226033 x = -0.7017226033 Simplifying x = -0.7017226033

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.2350559367, -0.7017226033}

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