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Simplifying -3x(-8 + -8x) + -6(x + -7) = 0 (-8 * -3x + -8x * -3x) + -6(x + -7) = 0 (24x + 24x2) + -6(x + -7) = 0 Reorder the terms: 24x + 24x2 + -6(-7 + x) = 0 24x + 24x2 + (-7 * -6 + x * -6) = 0 24x + 24x2 + (42 + -6x) = 0 Reorder the terms: 42 + 24x + -6x + 24x2 = 0 Combine like terms: 24x + -6x = 18x 42 + 18x + 24x2 = 0 Solving 42 + 18x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(7 + 3x + 4x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(7 + 3x + 4x2)' equal to zero and attempt to solve: Simplifying 7 + 3x + 4x2 = 0 Solving 7 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + 0.75x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + 0.75x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + 0.75x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + 0.75x + x2 = 0 + -1.75 0.75x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 0.75x + x2 = -1.75 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = -1.75 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = -1.75 + 0.140625 Combine like terms: -1.75 + 0.140625 = -1.609375 0.140625 + 0.75x + x2 = -1.609375 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = -1.609375 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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