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Simplifying 3x(-1x + -3) + -2 = x(3x + -4) + 13 Reorder the terms: 3x(-3 + -1x) + -2 = x(3x + -4) + 13 (-3 * 3x + -1x * 3x) + -2 = x(3x + -4) + 13 (-9x + -3x2) + -2 = x(3x + -4) + 13 Reorder the terms: -2 + -9x + -3x2 = x(3x + -4) + 13 Reorder the terms: -2 + -9x + -3x2 = x(-4 + 3x) + 13 -2 + -9x + -3x2 = (-4 * x + 3x * x) + 13 -2 + -9x + -3x2 = (-4x + 3x2) + 13 Reorder the terms: -2 + -9x + -3x2 = 13 + -4x + 3x2 Solving -2 + -9x + -3x2 = 13 + -4x + 3x2 Solving for variable 'x'. Reorder the terms: -2 + -13 + -9x + 4x + -3x2 + -3x2 = 13 + -4x + 3x2 + -13 + 4x + -3x2 Combine like terms: -2 + -13 = -15 -15 + -9x + 4x + -3x2 + -3x2 = 13 + -4x + 3x2 + -13 + 4x + -3x2 Combine like terms: -9x + 4x = -5x -15 + -5x + -3x2 + -3x2 = 13 + -4x + 3x2 + -13 + 4x + -3x2 Combine like terms: -3x2 + -3x2 = -6x2 -15 + -5x + -6x2 = 13 + -4x + 3x2 + -13 + 4x + -3x2 Reorder the terms: -15 + -5x + -6x2 = 13 + -13 + -4x + 4x + 3x2 + -3x2 Combine like terms: 13 + -13 = 0 -15 + -5x + -6x2 = 0 + -4x + 4x + 3x2 + -3x2 -15 + -5x + -6x2 = -4x + 4x + 3x2 + -3x2 Combine like terms: -4x + 4x = 0 -15 + -5x + -6x2 = 0 + 3x2 + -3x2 -15 + -5x + -6x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -15 + -5x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 5x + 6x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(15 + 5x + 6x2)' equal to zero and attempt to solve: Simplifying 15 + 5x + 6x2 = 0 Solving 15 + 5x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 2.5 + 0.8333333333x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 0.8333333333x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 0.8333333333x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 0.8333333333x + x2 = 0 + -2.5 0.8333333333x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 0.8333333333x + x2 = -2.5 The x term is 0.8333333333x. Take half its coefficient (0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. 0.8333333333x + 0.1736111111 + x2 = -2.5 + 0.1736111111 Reorder the terms: 0.1736111111 + 0.8333333333x + x2 = -2.5 + 0.1736111111 Combine like terms: -2.5 + 0.1736111111 = -2.3263888889 0.1736111111 + 0.8333333333x + x2 = -2.3263888889 Factor a perfect square on the left side: (x + 0.4166666667)(x + 0.4166666667) = -2.3263888889 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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