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Simplifying x2 + -3 = 13x2 + 8x Reorder the terms: -3 + x2 = 13x2 + 8x Reorder the terms: -3 + x2 = 8x + 13x2 Solving -3 + x2 = 8x + 13x2 Solving for variable 'x'. Reorder the terms: -3 + -8x + x2 + -13x2 = 8x + 13x2 + -8x + -13x2 Combine like terms: x2 + -13x2 = -12x2 -3 + -8x + -12x2 = 8x + 13x2 + -8x + -13x2 Reorder the terms: -3 + -8x + -12x2 = 8x + -8x + 13x2 + -13x2 Combine like terms: 8x + -8x = 0 -3 + -8x + -12x2 = 0 + 13x2 + -13x2 -3 + -8x + -12x2 = 13x2 + -13x2 Combine like terms: 13x2 + -13x2 = 0 -3 + -8x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 8x + 12x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 8x + 12x2)' equal to zero and attempt to solve: Simplifying 3 + 8x + 12x2 = 0 Solving 3 + 8x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.25 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 0.6666666667x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 0.6666666667x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 0.6666666667x + x2 = 0 + -0.25 0.6666666667x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 0.6666666667x + x2 = -0.25 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 = -0.25 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = -0.25 + 0.1111111112 Combine like terms: -0.25 + 0.1111111112 = -0.1388888888 0.1111111112 + 0.6666666667x + x2 = -0.1388888888 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = -0.1388888888 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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