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Simplifying 0 = 8x2 + 14x + 41 Reorder the terms: 0 = 41 + 14x + 8x2 Solving 0 = 41 + 14x + 8x2 Solving for variable 'x'. Combine like terms: 0 + -41 = -41 -41 + -14x + -8x2 = 41 + 14x + 8x2 + -41 + -14x + -8x2 Reorder the terms: -41 + -14x + -8x2 = 41 + -41 + 14x + -14x + 8x2 + -8x2 Combine like terms: 41 + -41 = 0 -41 + -14x + -8x2 = 0 + 14x + -14x + 8x2 + -8x2 -41 + -14x + -8x2 = 14x + -14x + 8x2 + -8x2 Combine like terms: 14x + -14x = 0 -41 + -14x + -8x2 = 0 + 8x2 + -8x2 -41 + -14x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -41 + -14x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(41 + 14x + 8x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(41 + 14x + 8x2)' equal to zero and attempt to solve: Simplifying 41 + 14x + 8x2 = 0 Solving 41 + 14x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 5.125 + 1.75x + x2 = 0 Move the constant term to the right: Add '-5.125' to each side of the equation. 5.125 + 1.75x + -5.125 + x2 = 0 + -5.125 Reorder the terms: 5.125 + -5.125 + 1.75x + x2 = 0 + -5.125 Combine like terms: 5.125 + -5.125 = 0.000 0.000 + 1.75x + x2 = 0 + -5.125 1.75x + x2 = 0 + -5.125 Combine like terms: 0 + -5.125 = -5.125 1.75x + x2 = -5.125 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = -5.125 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = -5.125 + 0.765625 Combine like terms: -5.125 + 0.765625 = -4.359375 0.765625 + 1.75x + x2 = -4.359375 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = -4.359375 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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