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Simplifying 8x + -2x(x + 9) = x + 47 Reorder the terms: 8x + -2x(9 + x) = x + 47 8x + (9 * -2x + x * -2x) = x + 47 8x + (-18x + -2x2) = x + 47 Combine like terms: 8x + -18x = -10x -10x + -2x2 = x + 47 Reorder the terms: -10x + -2x2 = 47 + x Solving -10x + -2x2 = 47 + x Solving for variable 'x'. Reorder the terms: -47 + -10x + -1x + -2x2 = 47 + x + -47 + -1x Combine like terms: -10x + -1x = -11x -47 + -11x + -2x2 = 47 + x + -47 + -1x Reorder the terms: -47 + -11x + -2x2 = 47 + -47 + x + -1x Combine like terms: 47 + -47 = 0 -47 + -11x + -2x2 = 0 + x + -1x -47 + -11x + -2x2 = x + -1x Combine like terms: x + -1x = 0 -47 + -11x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(47 + 11x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(47 + 11x + 2x2)' equal to zero and attempt to solve: Simplifying 47 + 11x + 2x2 = 0 Solving 47 + 11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 23.5 + 5.5x + x2 = 0 Move the constant term to the right: Add '-23.5' to each side of the equation. 23.5 + 5.5x + -23.5 + x2 = 0 + -23.5 Reorder the terms: 23.5 + -23.5 + 5.5x + x2 = 0 + -23.5 Combine like terms: 23.5 + -23.5 = 0.0 0.0 + 5.5x + x2 = 0 + -23.5 5.5x + x2 = 0 + -23.5 Combine like terms: 0 + -23.5 = -23.5 5.5x + x2 = -23.5 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = -23.5 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = -23.5 + 7.5625 Combine like terms: -23.5 + 7.5625 = -15.9375 7.5625 + 5.5x + x2 = -15.9375 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = -15.9375 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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