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Simplifying 14 + -2(3 + -4x) * x = 0 Reorder the terms for easier multiplication: 14 + -2x(3 + -4x) = 0 14 + (3 * -2x + -4x * -2x) = 0 14 + (-6x + 8x2) = 0 Solving 14 + -6x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + -3x + 4x2) = 0 Ignore the factor 2.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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