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Simplifying 6 + -4(x + 2) = 2x2 + 5x + 12 Reorder the terms: 6 + -4(2 + x) = 2x2 + 5x + 12 6 + (2 * -4 + x * -4) = 2x2 + 5x + 12 6 + (-8 + -4x) = 2x2 + 5x + 12 Combine like terms: 6 + -8 = -2 -2 + -4x = 2x2 + 5x + 12 Reorder the terms: -2 + -4x = 12 + 5x + 2x2 Solving -2 + -4x = 12 + 5x + 2x2 Solving for variable 'x'. Reorder the terms: -2 + -12 + -4x + -5x + -2x2 = 12 + 5x + 2x2 + -12 + -5x + -2x2 Combine like terms: -2 + -12 = -14 -14 + -4x + -5x + -2x2 = 12 + 5x + 2x2 + -12 + -5x + -2x2 Combine like terms: -4x + -5x = -9x -14 + -9x + -2x2 = 12 + 5x + 2x2 + -12 + -5x + -2x2 Reorder the terms: -14 + -9x + -2x2 = 12 + -12 + 5x + -5x + 2x2 + -2x2 Combine like terms: 12 + -12 = 0 -14 + -9x + -2x2 = 0 + 5x + -5x + 2x2 + -2x2 -14 + -9x + -2x2 = 5x + -5x + 2x2 + -2x2 Combine like terms: 5x + -5x = 0 -14 + -9x + -2x2 = 0 + 2x2 + -2x2 -14 + -9x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -14 + -9x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(14 + 9x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(14 + 9x + 2x2)' equal to zero and attempt to solve: Simplifying 14 + 9x + 2x2 = 0 Solving 14 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7 + 4.5x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + 4.5x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 4.5x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4.5x + x2 = 0 + -7 4.5x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 4.5x + x2 = -7 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = -7 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = -7 + 5.0625 Combine like terms: -7 + 5.0625 = -1.9375 5.0625 + 4.5x + x2 = -1.9375 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = -1.9375 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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