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Simplifying 8x(x + 2) = 2x + -24 Reorder the terms: 8x(2 + x) = 2x + -24 (2 * 8x + x * 8x) = 2x + -24 (16x + 8x2) = 2x + -24 Reorder the terms: 16x + 8x2 = -24 + 2x Solving 16x + 8x2 = -24 + 2x Solving for variable 'x'. Reorder the terms: 24 + 16x + -2x + 8x2 = -24 + 2x + 24 + -2x Combine like terms: 16x + -2x = 14x 24 + 14x + 8x2 = -24 + 2x + 24 + -2x Reorder the terms: 24 + 14x + 8x2 = -24 + 24 + 2x + -2x Combine like terms: -24 + 24 = 0 24 + 14x + 8x2 = 0 + 2x + -2x 24 + 14x + 8x2 = 2x + -2x Combine like terms: 2x + -2x = 0 24 + 14x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 7x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + 7x + 4x2)' equal to zero and attempt to solve: Simplifying 12 + 7x + 4x2 = 0 Solving 12 + 7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3 + 1.75x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 1.75x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 1.75x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 1.75x + x2 = 0 + -3 1.75x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 1.75x + x2 = -3 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = -3 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = -3 + 0.765625 Combine like terms: -3 + 0.765625 = -2.234375 0.765625 + 1.75x + x2 = -2.234375 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = -2.234375 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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