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Simplifying 0 = -16x2 + 10x + -30 Reorder the terms: 0 = -30 + 10x + -16x2 Solving 0 = -30 + 10x + -16x2 Solving for variable 'x'. Combine like terms: 0 + 30 = 30 30 + -10x + 16x2 = -30 + 10x + -16x2 + 30 + -10x + 16x2 Reorder the terms: 30 + -10x + 16x2 = -30 + 30 + 10x + -10x + -16x2 + 16x2 Combine like terms: -30 + 30 = 0 30 + -10x + 16x2 = 0 + 10x + -10x + -16x2 + 16x2 30 + -10x + 16x2 = 10x + -10x + -16x2 + 16x2 Combine like terms: 10x + -10x = 0 30 + -10x + 16x2 = 0 + -16x2 + 16x2 30 + -10x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 30 + -10x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -5x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + -5x + 8x2)' equal to zero and attempt to solve: Simplifying 15 + -5x + 8x2 = 0 Solving 15 + -5x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.875 + -0.625x + x2 = 0 Move the constant term to the right: Add '-1.875' to each side of the equation. 1.875 + -0.625x + -1.875 + x2 = 0 + -1.875 Reorder the terms: 1.875 + -1.875 + -0.625x + x2 = 0 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + -0.625x + x2 = 0 + -1.875 -0.625x + x2 = 0 + -1.875 Combine like terms: 0 + -1.875 = -1.875 -0.625x + x2 = -1.875 The x term is -0.625x. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625x + 0.09765625 + x2 = -1.875 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = -1.875 + 0.09765625 Combine like terms: -1.875 + 0.09765625 = -1.77734375 0.09765625 + -0.625x + x2 = -1.77734375 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = -1.77734375 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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