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Simplifying 17x2 + 576 = x(x + 118) + -46x Reorder the terms: 576 + 17x2 = x(x + 118) + -46x Reorder the terms: 576 + 17x2 = x(118 + x) + -46x 576 + 17x2 = (118 * x + x * x) + -46x 576 + 17x2 = (118x + x2) + -46x Reorder the terms: 576 + 17x2 = 118x + -46x + x2 Combine like terms: 118x + -46x = 72x 576 + 17x2 = 72x + x2 Solving 576 + 17x2 = 72x + x2 Solving for variable 'x'. Reorder the terms: 576 + -72x + 17x2 + -1x2 = 72x + x2 + -72x + -1x2 Combine like terms: 17x2 + -1x2 = 16x2 576 + -72x + 16x2 = 72x + x2 + -72x + -1x2 Reorder the terms: 576 + -72x + 16x2 = 72x + -72x + x2 + -1x2 Combine like terms: 72x + -72x = 0 576 + -72x + 16x2 = 0 + x2 + -1x2 576 + -72x + 16x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 576 + -72x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(72 + -9x + 2x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(72 + -9x + 2x2)' equal to zero and attempt to solve: Simplifying 72 + -9x + 2x2 = 0 Solving 72 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 36 + -4.5x + x2 = 0 Move the constant term to the right: Add '-36' to each side of the equation. 36 + -4.5x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -4.5x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -4.5x + x2 = 0 + -36 -4.5x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -4.5x + x2 = -36 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = -36 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -36 + 5.0625 Combine like terms: -36 + 5.0625 = -30.9375 5.0625 + -4.5x + x2 = -30.9375 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = -30.9375 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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