0=15x^2+15x-7

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Solution for 0=15x^2+15x-7 equation:


Simplifying
0 = 15x2 + 15x + -7

Reorder the terms:
0 = -7 + 15x + 15x2

Solving
0 = -7 + 15x + 15x2

Solving for variable 'x'.

Combine like terms: 0 + 7 = 7
7 + -15x + -15x2 = -7 + 15x + 15x2 + 7 + -15x + -15x2

Reorder the terms:
7 + -15x + -15x2 = -7 + 7 + 15x + -15x + 15x2 + -15x2

Combine like terms: -7 + 7 = 0
7 + -15x + -15x2 = 0 + 15x + -15x + 15x2 + -15x2
7 + -15x + -15x2 = 15x + -15x + 15x2 + -15x2

Combine like terms: 15x + -15x = 0
7 + -15x + -15x2 = 0 + 15x2 + -15x2
7 + -15x + -15x2 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
7 + -15x + -15x2 = 0

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

Divide each side by '-15'.
-0.4666666667 + x + x2 = 0

Move the constant term to the right:

Add '0.4666666667' to each side of the equation.
-0.4666666667 + x + 0.4666666667 + x2 = 0 + 0.4666666667

Reorder the terms:
-0.4666666667 + 0.4666666667 + x + x2 = 0 + 0.4666666667

Combine like terms: -0.4666666667 + 0.4666666667 = 0.0000000000
0.0000000000 + x + x2 = 0 + 0.4666666667
x + x2 = 0 + 0.4666666667

Combine like terms: 0 + 0.4666666667 = 0.4666666667
x + x2 = 0.4666666667

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 0.4666666667 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 0.4666666667 + 0.25

Combine like terms: 0.4666666667 + 0.25 = 0.7166666667
1.25 + x2 = 0.7166666667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.7166666667

Calculate the square root of the right side: 0.846561673

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.846561673 and -0.846561673.

Subproblem 1

x + 0.5 = 0.846561673 Simplifying x + 0.5 = 0.846561673 Reorder the terms: 0.5 + x = 0.846561673 Solving 0.5 + x = 0.846561673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.846561673 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.846561673 + -0.5 x = 0.846561673 + -0.5 Combine like terms: 0.846561673 + -0.5 = 0.346561673 x = 0.346561673 Simplifying x = 0.346561673

Subproblem 2

x + 0.5 = -0.846561673 Simplifying x + 0.5 = -0.846561673 Reorder the terms: 0.5 + x = -0.846561673 Solving 0.5 + x = -0.846561673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.846561673 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.846561673 + -0.5 x = -0.846561673 + -0.5 Combine like terms: -0.846561673 + -0.5 = -1.346561673 x = -1.346561673 Simplifying x = -1.346561673

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.346561673, -1.346561673}

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