8x^2+5x-13=-4x^2-3x

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Solution for 8x^2+5x-13=-4x^2-3x equation:


Simplifying
8x2 + 5x + -13 = -4x2 + -3x

Reorder the terms:
-13 + 5x + 8x2 = -4x2 + -3x

Reorder the terms:
-13 + 5x + 8x2 = -3x + -4x2

Solving
-13 + 5x + 8x2 = -3x + -4x2

Solving for variable 'x'.

Reorder the terms:
-13 + 5x + 3x + 8x2 + 4x2 = -3x + -4x2 + 3x + 4x2

Combine like terms: 5x + 3x = 8x
-13 + 8x + 8x2 + 4x2 = -3x + -4x2 + 3x + 4x2

Combine like terms: 8x2 + 4x2 = 12x2
-13 + 8x + 12x2 = -3x + -4x2 + 3x + 4x2

Reorder the terms:
-13 + 8x + 12x2 = -3x + 3x + -4x2 + 4x2

Combine like terms: -3x + 3x = 0
-13 + 8x + 12x2 = 0 + -4x2 + 4x2
-13 + 8x + 12x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-13 + 8x + 12x2 = 0

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

Divide each side by '12'.
-1.083333333 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '1.083333333' to each side of the equation.
-1.083333333 + 0.6666666667x + 1.083333333 + x2 = 0 + 1.083333333

Reorder the terms:
-1.083333333 + 1.083333333 + 0.6666666667x + x2 = 0 + 1.083333333

Combine like terms: -1.083333333 + 1.083333333 = 0.000000000
0.000000000 + 0.6666666667x + x2 = 0 + 1.083333333
0.6666666667x + x2 = 0 + 1.083333333

Combine like terms: 0 + 1.083333333 = 1.083333333
0.6666666667x + x2 = 1.083333333

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 1.083333333 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 1.083333333 + 0.1111111112

Combine like terms: 1.083333333 + 0.1111111112 = 1.1944444442
0.1111111112 + 0.6666666667x + x2 = 1.1944444442

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 1.1944444442

Calculate the square root of the right side: 1.092906421

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 1.092906421 and -1.092906421.

Subproblem 1

x + 0.3333333334 = 1.092906421 Simplifying x + 0.3333333334 = 1.092906421 Reorder the terms: 0.3333333334 + x = 1.092906421 Solving 0.3333333334 + x = 1.092906421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 1.092906421 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 1.092906421 + -0.3333333334 x = 1.092906421 + -0.3333333334 Combine like terms: 1.092906421 + -0.3333333334 = 0.7595730876 x = 0.7595730876 Simplifying x = 0.7595730876

Subproblem 2

x + 0.3333333334 = -1.092906421 Simplifying x + 0.3333333334 = -1.092906421 Reorder the terms: 0.3333333334 + x = -1.092906421 Solving 0.3333333334 + x = -1.092906421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -1.092906421 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -1.092906421 + -0.3333333334 x = -1.092906421 + -0.3333333334 Combine like terms: -1.092906421 + -0.3333333334 = -1.4262397544 x = -1.4262397544 Simplifying x = -1.4262397544

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.7595730876, -1.4262397544}

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