15x^2+14x-60=0

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Solution for 15x^2+14x-60=0 equation:


Simplifying
15x2 + 14x + -60 = 0

Reorder the terms:
-60 + 14x + 15x2 = 0

Solving
-60 + 14x + 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'.
-4 + 0.9333333333x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 0.9333333333x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 0.9333333333x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 0.9333333333x + x2 = 0 + 4
0.9333333333x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
0.9333333333x + x2 = 4

The x term is 0.9333333333x.  Take half its coefficient (0.4666666667).
Square it (0.2177777778) and add it to both sides.

Add '0.2177777778' to each side of the equation.
0.9333333333x + 0.2177777778 + x2 = 4 + 0.2177777778

Reorder the terms:
0.2177777778 + 0.9333333333x + x2 = 4 + 0.2177777778

Combine like terms: 4 + 0.2177777778 = 4.2177777778
0.2177777778 + 0.9333333333x + x2 = 4.2177777778

Factor a perfect square on the left side:
(x + 0.4666666667)(x + 0.4666666667) = 4.2177777778

Calculate the square root of the right side: 2.053722907

Break this problem into two subproblems by setting 
(x + 0.4666666667) equal to 2.053722907 and -2.053722907.

Subproblem 1

x + 0.4666666667 = 2.053722907 Simplifying x + 0.4666666667 = 2.053722907 Reorder the terms: 0.4666666667 + x = 2.053722907 Solving 0.4666666667 + x = 2.053722907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4666666667' to each side of the equation. 0.4666666667 + -0.4666666667 + x = 2.053722907 + -0.4666666667 Combine like terms: 0.4666666667 + -0.4666666667 = 0.0000000000 0.0000000000 + x = 2.053722907 + -0.4666666667 x = 2.053722907 + -0.4666666667 Combine like terms: 2.053722907 + -0.4666666667 = 1.5870562403 x = 1.5870562403 Simplifying x = 1.5870562403

Subproblem 2

x + 0.4666666667 = -2.053722907 Simplifying x + 0.4666666667 = -2.053722907 Reorder the terms: 0.4666666667 + x = -2.053722907 Solving 0.4666666667 + x = -2.053722907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4666666667' to each side of the equation. 0.4666666667 + -0.4666666667 + x = -2.053722907 + -0.4666666667 Combine like terms: 0.4666666667 + -0.4666666667 = 0.0000000000 0.0000000000 + x = -2.053722907 + -0.4666666667 x = -2.053722907 + -0.4666666667 Combine like terms: -2.053722907 + -0.4666666667 = -2.5203895737 x = -2.5203895737 Simplifying x = -2.5203895737

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.5870562403, -2.5203895737}

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