(2x-13x^2+3)-(2x^2+8x)=0

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Solution for (2x-13x^2+3)-(2x^2+8x)=0 equation:


Simplifying
(2x + -13x2 + 3) + -1(2x2 + 8x) = 0

Reorder the terms:
(3 + 2x + -13x2) + -1(2x2 + 8x) = 0

Remove parenthesis around (3 + 2x + -13x2)
3 + 2x + -13x2 + -1(2x2 + 8x) = 0

Reorder the terms:
3 + 2x + -13x2 + -1(8x + 2x2) = 0
3 + 2x + -13x2 + (8x * -1 + 2x2 * -1) = 0
3 + 2x + -13x2 + (-8x + -2x2) = 0

Reorder the terms:
3 + 2x + -8x + -13x2 + -2x2 = 0

Combine like terms: 2x + -8x = -6x
3 + -6x + -13x2 + -2x2 = 0

Combine like terms: -13x2 + -2x2 = -15x2
3 + -6x + -15x2 = 0

Solving
3 + -6x + -15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -2x + -5x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(1 + -2x + -5x2)' equal to zero and attempt to solve: Simplifying 1 + -2x + -5x2 = 0 Solving 1 + -2x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.2 + 0.4x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 0.4x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 0.4x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 0.4x + x2 = 0 + 0.2 0.4x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 0.4x + x2 = 0.2 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 0.2 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 0.2 + 0.04 Combine like terms: 0.2 + 0.04 = 0.24 0.04 + 0.4x + x2 = 0.24 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 0.24 Calculate the square root of the right side: 0.489897949 Break this problem into two subproblems by setting (x + 0.2) equal to 0.489897949 and -0.489897949.

Subproblem 1

x + 0.2 = 0.489897949 Simplifying x + 0.2 = 0.489897949 Reorder the terms: 0.2 + x = 0.489897949 Solving 0.2 + x = 0.489897949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 0.489897949 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.489897949 + -0.2 x = 0.489897949 + -0.2 Combine like terms: 0.489897949 + -0.2 = 0.289897949 x = 0.289897949 Simplifying x = 0.289897949

Subproblem 2

x + 0.2 = -0.489897949 Simplifying x + 0.2 = -0.489897949 Reorder the terms: 0.2 + x = -0.489897949 Solving 0.2 + x = -0.489897949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -0.489897949 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.489897949 + -0.2 x = -0.489897949 + -0.2 Combine like terms: -0.489897949 + -0.2 = -0.689897949 x = -0.689897949 Simplifying x = -0.689897949

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.289897949, -0.689897949}

Solution

x = {0.289897949, -0.689897949}

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