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Simplifying 16x2 + 90x + 144 = 0 Reorder the terms: 144 + 90x + 16x2 = 0 Solving 144 + 90x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(72 + 45x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(72 + 45x + 8x2)' equal to zero and attempt to solve: Simplifying 72 + 45x + 8x2 = 0 Solving 72 + 45x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 9 + 5.625x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + 5.625x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 5.625x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 5.625x + x2 = 0 + -9 5.625x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 5.625x + x2 = -9 The x term is 5.625x. Take half its coefficient (2.8125). Square it (7.91015625) and add it to both sides. Add '7.91015625' to each side of the equation. 5.625x + 7.91015625 + x2 = -9 + 7.91015625 Reorder the terms: 7.91015625 + 5.625x + x2 = -9 + 7.91015625 Combine like terms: -9 + 7.91015625 = -1.08984375 7.91015625 + 5.625x + x2 = -1.08984375 Factor a perfect square on the left side: (x + 2.8125)(x + 2.8125) = -1.08984375 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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