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Simplifying 3(x + 1) = 2(x2 + 2x + 9) Reorder the terms: 3(1 + x) = 2(x2 + 2x + 9) (1 * 3 + x * 3) = 2(x2 + 2x + 9) (3 + 3x) = 2(x2 + 2x + 9) Reorder the terms: 3 + 3x = 2(9 + 2x + x2) 3 + 3x = (9 * 2 + 2x * 2 + x2 * 2) 3 + 3x = (18 + 4x + 2x2) Solving 3 + 3x = 18 + 4x + 2x2 Solving for variable 'x'. Reorder the terms: 3 + -18 + 3x + -4x + -2x2 = 18 + 4x + 2x2 + -18 + -4x + -2x2 Combine like terms: 3 + -18 = -15 -15 + 3x + -4x + -2x2 = 18 + 4x + 2x2 + -18 + -4x + -2x2 Combine like terms: 3x + -4x = -1x -15 + -1x + -2x2 = 18 + 4x + 2x2 + -18 + -4x + -2x2 Reorder the terms: -15 + -1x + -2x2 = 18 + -18 + 4x + -4x + 2x2 + -2x2 Combine like terms: 18 + -18 = 0 -15 + -1x + -2x2 = 0 + 4x + -4x + 2x2 + -2x2 -15 + -1x + -2x2 = 4x + -4x + 2x2 + -2x2 Combine like terms: 4x + -4x = 0 -15 + -1x + -2x2 = 0 + 2x2 + -2x2 -15 + -1x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -15 + -1x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(15 + x + 2x2)' equal to zero and attempt to solve: Simplifying 15 + x + 2x2 = 0 Solving 15 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + 0.5x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + 0.5x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + 0.5x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + 0.5x + x2 = 0 + -7.5 0.5x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 0.5x + x2 = -7.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5x + 0.25 + x2 = -7.5 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = -7.5 + 0.25 Combine like terms: -7.5 + 0.25 = -7.25 0.25 + 0.5x + x2 = -7.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -7.25 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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