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Simplifying 14x2 + 2x + 12 + -4x + 2x2 = 0 Reorder the terms: 12 + 2x + -4x + 14x2 + 2x2 = 0 Combine like terms: 2x + -4x = -2x 12 + -2x + 14x2 + 2x2 = 0 Combine like terms: 14x2 + 2x2 = 16x2 12 + -2x + 16x2 = 0 Solving 12 + -2x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -1x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -1x + 8x2)' equal to zero and attempt to solve: Simplifying 6 + -1x + 8x2 = 0 Solving 6 + -1x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.75 + -0.125x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -0.125x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -0.125x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -0.125x + x2 = 0 + -0.75 -0.125x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -0.125x + x2 = -0.75 The x term is -0.125x. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125x + 0.00390625 + x2 = -0.75 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x + x2 = -0.75 + 0.00390625 Combine like terms: -0.75 + 0.00390625 = -0.74609375 0.00390625 + -0.125x + x2 = -0.74609375 Factor a perfect square on the left side: (x + -0.0625)(x + -0.0625) = -0.74609375 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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