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Simplifying 0 = 8x2 + 17x + 10 Reorder the terms: 0 = 10 + 17x + 8x2 Solving 0 = 10 + 17x + 8x2 Solving for variable 'x'. Combine like terms: 0 + -10 = -10 -10 + -17x + -8x2 = 10 + 17x + 8x2 + -10 + -17x + -8x2 Reorder the terms: -10 + -17x + -8x2 = 10 + -10 + 17x + -17x + 8x2 + -8x2 Combine like terms: 10 + -10 = 0 -10 + -17x + -8x2 = 0 + 17x + -17x + 8x2 + -8x2 -10 + -17x + -8x2 = 17x + -17x + 8x2 + -8x2 Combine like terms: 17x + -17x = 0 -10 + -17x + -8x2 = 0 + 8x2 + -8x2 -10 + -17x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -10 + -17x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(10 + 17x + 8x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(10 + 17x + 8x2)' equal to zero and attempt to solve: Simplifying 10 + 17x + 8x2 = 0 Solving 10 + 17x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.25 + 2.125x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 2.125x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 2.125x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 2.125x + x2 = 0 + -1.25 2.125x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 2.125x + x2 = -1.25 The x term is 2.125x. Take half its coefficient (1.0625). Square it (1.12890625) and add it to both sides. Add '1.12890625' to each side of the equation. 2.125x + 1.12890625 + x2 = -1.25 + 1.12890625 Reorder the terms: 1.12890625 + 2.125x + x2 = -1.25 + 1.12890625 Combine like terms: -1.25 + 1.12890625 = -0.12109375 1.12890625 + 2.125x + x2 = -0.12109375 Factor a perfect square on the left side: (x + 1.0625)(x + 1.0625) = -0.12109375 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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