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Simplifying 3x + -7 = 8 + 6x(x + 2) Reorder the terms: -7 + 3x = 8 + 6x(x + 2) Reorder the terms: -7 + 3x = 8 + 6x(2 + x) -7 + 3x = 8 + (2 * 6x + x * 6x) -7 + 3x = 8 + (12x + 6x2) Solving -7 + 3x = 8 + 12x + 6x2 Solving for variable 'x'. Reorder the terms: -7 + -8 + 3x + -12x + -6x2 = 8 + 12x + 6x2 + -8 + -12x + -6x2 Combine like terms: -7 + -8 = -15 -15 + 3x + -12x + -6x2 = 8 + 12x + 6x2 + -8 + -12x + -6x2 Combine like terms: 3x + -12x = -9x -15 + -9x + -6x2 = 8 + 12x + 6x2 + -8 + -12x + -6x2 Reorder the terms: -15 + -9x + -6x2 = 8 + -8 + 12x + -12x + 6x2 + -6x2 Combine like terms: 8 + -8 = 0 -15 + -9x + -6x2 = 0 + 12x + -12x + 6x2 + -6x2 -15 + -9x + -6x2 = 12x + -12x + 6x2 + -6x2 Combine like terms: 12x + -12x = 0 -15 + -9x + -6x2 = 0 + 6x2 + -6x2 -15 + -9x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -15 + -9x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(5 + 3x + 2x2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(5 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying 5 + 3x + 2x2 = 0 Solving 5 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 1.5x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 1.5x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 1.5x + x2 = 0 + -2.5 1.5x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 1.5x + x2 = -2.5 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = -2.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -2.5 + 0.5625 Combine like terms: -2.5 + 0.5625 = -1.9375 0.5625 + 1.5x + x2 = -1.9375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -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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