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Simplifying -2(x) = 3x2 + 5x + 12 Reorder the terms: -2x = 12 + 5x + 3x2 Solving -2x = 12 + 5x + 3x2 Solving for variable 'x'. Reorder the terms: -12 + -2x + -5x + -3x2 = 12 + 5x + 3x2 + -12 + -5x + -3x2 Combine like terms: -2x + -5x = -7x -12 + -7x + -3x2 = 12 + 5x + 3x2 + -12 + -5x + -3x2 Reorder the terms: -12 + -7x + -3x2 = 12 + -12 + 5x + -5x + 3x2 + -3x2 Combine like terms: 12 + -12 = 0 -12 + -7x + -3x2 = 0 + 5x + -5x + 3x2 + -3x2 -12 + -7x + -3x2 = 5x + -5x + 3x2 + -3x2 Combine like terms: 5x + -5x = 0 -12 + -7x + -3x2 = 0 + 3x2 + -3x2 -12 + -7x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -12 + -7x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 7x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + 7x + 3x2)' equal to zero and attempt to solve: Simplifying 12 + 7x + 3x2 = 0 Solving 12 + 7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 2.333333333x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 2.333333333x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 2.333333333x + x2 = 0 + -4 2.333333333x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 2.333333333x + x2 = -4 The x term is 2.333333333x. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333x + 1.361111112 + x2 = -4 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = -4 + 1.361111112 Combine like terms: -4 + 1.361111112 = -2.638888888 1.361111112 + 2.333333333x + x2 = -2.638888888 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = -2.638888888 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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