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Simplifying 2x2 + -12x + -9 + -15 + -3x = 4x2 + -8x Reorder the terms: -9 + -15 + -12x + -3x + 2x2 = 4x2 + -8x Combine like terms: -9 + -15 = -24 -24 + -12x + -3x + 2x2 = 4x2 + -8x Combine like terms: -12x + -3x = -15x -24 + -15x + 2x2 = 4x2 + -8x Reorder the terms: -24 + -15x + 2x2 = -8x + 4x2 Solving -24 + -15x + 2x2 = -8x + 4x2 Solving for variable 'x'. Reorder the terms: -24 + -15x + 8x + 2x2 + -4x2 = -8x + 4x2 + 8x + -4x2 Combine like terms: -15x + 8x = -7x -24 + -7x + 2x2 + -4x2 = -8x + 4x2 + 8x + -4x2 Combine like terms: 2x2 + -4x2 = -2x2 -24 + -7x + -2x2 = -8x + 4x2 + 8x + -4x2 Reorder the terms: -24 + -7x + -2x2 = -8x + 8x + 4x2 + -4x2 Combine like terms: -8x + 8x = 0 -24 + -7x + -2x2 = 0 + 4x2 + -4x2 -24 + -7x + -2x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -24 + -7x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(24 + 7x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(24 + 7x + 2x2)' equal to zero and attempt to solve: Simplifying 24 + 7x + 2x2 = 0 Solving 24 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 12 + 3.5x + x2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + 3.5x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + 3.5x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 3.5x + x2 = 0 + -12 3.5x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 3.5x + x2 = -12 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = -12 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = -12 + 3.0625 Combine like terms: -12 + 3.0625 = -8.9375 3.0625 + 3.5x + x2 = -8.9375 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = -8.9375 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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