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Simplifying 0 = 2x2 + 10x + 17 Reorder the terms: 0 = 17 + 10x + 2x2 Solving 0 = 17 + 10x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -17 = -17 -17 + -10x + -2x2 = 17 + 10x + 2x2 + -17 + -10x + -2x2 Reorder the terms: -17 + -10x + -2x2 = 17 + -17 + 10x + -10x + 2x2 + -2x2 Combine like terms: 17 + -17 = 0 -17 + -10x + -2x2 = 0 + 10x + -10x + 2x2 + -2x2 -17 + -10x + -2x2 = 10x + -10x + 2x2 + -2x2 Combine like terms: 10x + -10x = 0 -17 + -10x + -2x2 = 0 + 2x2 + -2x2 -17 + -10x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -17 + -10x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(17 + 10x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(17 + 10x + 2x2)' equal to zero and attempt to solve: Simplifying 17 + 10x + 2x2 = 0 Solving 17 + 10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8.5 + 5x + x2 = 0 Move the constant term to the right: Add '-8.5' to each side of the equation. 8.5 + 5x + -8.5 + x2 = 0 + -8.5 Reorder the terms: 8.5 + -8.5 + 5x + x2 = 0 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + 5x + x2 = 0 + -8.5 5x + x2 = 0 + -8.5 Combine like terms: 0 + -8.5 = -8.5 5x + x2 = -8.5 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -8.5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -8.5 + 6.25 Combine like terms: -8.5 + 6.25 = -2.25 6.25 + 5x + x2 = -2.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = -2.25 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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