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Simplifying -16x2 + 6x = 56 Reorder the terms: 6x + -16x2 = 56 Solving 6x + -16x2 = 56 Solving for variable 'x'. Reorder the terms: -56 + 6x + -16x2 = 56 + -56 Combine like terms: 56 + -56 = 0 -56 + 6x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-28 + 3x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-28 + 3x + -8x2)' equal to zero and attempt to solve: Simplifying -28 + 3x + -8x2 = 0 Solving -28 + 3x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 3.5 + -0.375x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -0.375x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -0.375x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -0.375x + x2 = 0 + -3.5 -0.375x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -0.375x + x2 = -3.5 The x term is -0.375x. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375x + 0.03515625 + x2 = -3.5 + 0.03515625 Reorder the terms: 0.03515625 + -0.375x + x2 = -3.5 + 0.03515625 Combine like terms: -3.5 + 0.03515625 = -3.46484375 0.03515625 + -0.375x + x2 = -3.46484375 Factor a perfect square on the left side: (x + -0.1875)(x + -0.1875) = -3.46484375 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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