5(x^2)-1=15(2x)-2

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Solution for 5(x^2)-1=15(2x)-2 equation:


Simplifying
5(x2) + -1 = 15(2x) + -2

Reorder the terms:
-1 + 5x2 = 15(2x) + -2

Remove parenthesis around (2x)
-1 + 5x2 = 15 * 2x + -2

Multiply 15 * 2
-1 + 5x2 = 30x + -2

Reorder the terms:
-1 + 5x2 = -2 + 30x

Solving
-1 + 5x2 = -2 + 30x

Solving for variable 'x'.

Reorder the terms:
-1 + 2 + -30x + 5x2 = -2 + 30x + 2 + -30x

Combine like terms: -1 + 2 = 1
1 + -30x + 5x2 = -2 + 30x + 2 + -30x

Reorder the terms:
1 + -30x + 5x2 = -2 + 2 + 30x + -30x

Combine like terms: -2 + 2 = 0
1 + -30x + 5x2 = 0 + 30x + -30x
1 + -30x + 5x2 = 30x + -30x

Combine like terms: 30x + -30x = 0
1 + -30x + 5x2 = 0

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

Divide each side by '5'.
0.2 + -6x + x2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -6x + -0.2 + x2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -6x + x2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -6x + x2 = 0 + -0.2
-6x + x2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-6x + x2 = -0.2

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -0.2 + 9

Reorder the terms:
9 + -6x + x2 = -0.2 + 9

Combine like terms: -0.2 + 9 = 8.8
9 + -6x + x2 = 8.8

Factor a perfect square on the left side:
(x + -3)(x + -3) = 8.8

Calculate the square root of the right side: 2.966479395

Break this problem into two subproblems by setting 
(x + -3) equal to 2.966479395 and -2.966479395.

Subproblem 1

x + -3 = 2.966479395 Simplifying x + -3 = 2.966479395 Reorder the terms: -3 + x = 2.966479395 Solving -3 + x = 2.966479395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.966479395 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.966479395 + 3 x = 2.966479395 + 3 Combine like terms: 2.966479395 + 3 = 5.966479395 x = 5.966479395 Simplifying x = 5.966479395

Subproblem 2

x + -3 = -2.966479395 Simplifying x + -3 = -2.966479395 Reorder the terms: -3 + x = -2.966479395 Solving -3 + x = -2.966479395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.966479395 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.966479395 + 3 x = -2.966479395 + 3 Combine like terms: -2.966479395 + 3 = 0.033520605 x = 0.033520605 Simplifying x = 0.033520605

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.966479395, 0.033520605}

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