15x^2+12=20+3x

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Solution for 15x^2+12=20+3x equation:


Simplifying
15x2 + 12 = 20 + 3x

Reorder the terms:
12 + 15x2 = 20 + 3x

Solving
12 + 15x2 = 20 + 3x

Solving for variable 'x'.

Reorder the terms:
12 + -20 + -3x + 15x2 = 20 + 3x + -20 + -3x

Combine like terms: 12 + -20 = -8
-8 + -3x + 15x2 = 20 + 3x + -20 + -3x

Reorder the terms:
-8 + -3x + 15x2 = 20 + -20 + 3x + -3x

Combine like terms: 20 + -20 = 0
-8 + -3x + 15x2 = 0 + 3x + -3x
-8 + -3x + 15x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-8 + -3x + 15x2 = 0

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

Divide each side by '15'.
-0.5333333333 + -0.2x + x2 = 0

Move the constant term to the right:

Add '0.5333333333' to each side of the equation.
-0.5333333333 + -0.2x + 0.5333333333 + x2 = 0 + 0.5333333333

Reorder the terms:
-0.5333333333 + 0.5333333333 + -0.2x + x2 = 0 + 0.5333333333

Combine like terms: -0.5333333333 + 0.5333333333 = 0.0000000000
0.0000000000 + -0.2x + x2 = 0 + 0.5333333333
-0.2x + x2 = 0 + 0.5333333333

Combine like terms: 0 + 0.5333333333 = 0.5333333333
-0.2x + x2 = 0.5333333333

The x term is -0.2x.  Take half its coefficient (-0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
-0.2x + 0.01 + x2 = 0.5333333333 + 0.01

Reorder the terms:
0.01 + -0.2x + x2 = 0.5333333333 + 0.01

Combine like terms: 0.5333333333 + 0.01 = 0.5433333333
0.01 + -0.2x + x2 = 0.5433333333

Factor a perfect square on the left side:
(x + -0.1)(x + -0.1) = 0.5433333333

Calculate the square root of the right side: 0.73711148

Break this problem into two subproblems by setting 
(x + -0.1) equal to 0.73711148 and -0.73711148.

Subproblem 1

x + -0.1 = 0.73711148 Simplifying x + -0.1 = 0.73711148 Reorder the terms: -0.1 + x = 0.73711148 Solving -0.1 + x = 0.73711148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 0.73711148 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 0.73711148 + 0.1 x = 0.73711148 + 0.1 Combine like terms: 0.73711148 + 0.1 = 0.83711148 x = 0.83711148 Simplifying x = 0.83711148

Subproblem 2

x + -0.1 = -0.73711148 Simplifying x + -0.1 = -0.73711148 Reorder the terms: -0.1 + x = -0.73711148 Solving -0.1 + x = -0.73711148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -0.73711148 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -0.73711148 + 0.1 x = -0.73711148 + 0.1 Combine like terms: -0.73711148 + 0.1 = -0.63711148 x = -0.63711148 Simplifying x = -0.63711148

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.83711148, -0.63711148}

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