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Simplifying 3x + 12 + -4x(2x + 3) = 6x + 25 Reorder the terms: 3x + 12 + -4x(3 + 2x) = 6x + 25 3x + 12 + (3 * -4x + 2x * -4x) = 6x + 25 3x + 12 + (-12x + -8x2) = 6x + 25 Reorder the terms: 12 + 3x + -12x + -8x2 = 6x + 25 Combine like terms: 3x + -12x = -9x 12 + -9x + -8x2 = 6x + 25 Reorder the terms: 12 + -9x + -8x2 = 25 + 6x Solving 12 + -9x + -8x2 = 25 + 6x Solving for variable 'x'. Reorder the terms: 12 + -25 + -9x + -6x + -8x2 = 25 + 6x + -25 + -6x Combine like terms: 12 + -25 = -13 -13 + -9x + -6x + -8x2 = 25 + 6x + -25 + -6x Combine like terms: -9x + -6x = -15x -13 + -15x + -8x2 = 25 + 6x + -25 + -6x Reorder the terms: -13 + -15x + -8x2 = 25 + -25 + 6x + -6x Combine like terms: 25 + -25 = 0 -13 + -15x + -8x2 = 0 + 6x + -6x -13 + -15x + -8x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -13 + -15x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(13 + 15x + 8x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(13 + 15x + 8x2)' equal to zero and attempt to solve: Simplifying 13 + 15x + 8x2 = 0 Solving 13 + 15x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.625 + 1.875x + x2 = 0 Move the constant term to the right: Add '-1.625' to each side of the equation. 1.625 + 1.875x + -1.625 + x2 = 0 + -1.625 Reorder the terms: 1.625 + -1.625 + 1.875x + x2 = 0 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + 1.875x + x2 = 0 + -1.625 1.875x + x2 = 0 + -1.625 Combine like terms: 0 + -1.625 = -1.625 1.875x + x2 = -1.625 The x term is 1.875x. Take half its coefficient (0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. 1.875x + 0.87890625 + x2 = -1.625 + 0.87890625 Reorder the terms: 0.87890625 + 1.875x + x2 = -1.625 + 0.87890625 Combine like terms: -1.625 + 0.87890625 = -0.74609375 0.87890625 + 1.875x + x2 = -0.74609375 Factor a perfect square on the left side: (x + 0.9375)(x + 0.9375) = -0.74609375 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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