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Simplifying 17 + -1(x + (x + -7)) = x2 + x2 + -14 + 49 Reorder the terms: 17 + -1(x + (-7 + x)) = x2 + x2 + -14 + 49 Remove parenthesis around (-7 + x) 17 + -1(x + -7 + x) = x2 + x2 + -14 + 49 Reorder the terms: 17 + -1(-7 + x + x) = x2 + x2 + -14 + 49 Combine like terms: x + x = 2x 17 + -1(-7 + 2x) = x2 + x2 + -14 + 49 17 + (-7 * -1 + 2x * -1) = x2 + x2 + -14 + 49 17 + (7 + -2x) = x2 + x2 + -14 + 49 Combine like terms: 17 + 7 = 24 24 + -2x = x2 + x2 + -14 + 49 Reorder the terms: 24 + -2x = -14 + 49 + x2 + x2 Combine like terms: -14 + 49 = 35 24 + -2x = 35 + x2 + x2 Combine like terms: x2 + x2 = 2x2 24 + -2x = 35 + 2x2 Solving 24 + -2x = 35 + 2x2 Solving for variable 'x'. Reorder the terms: 24 + -35 + -2x + -2x2 = 35 + 2x2 + -35 + -2x2 Combine like terms: 24 + -35 = -11 -11 + -2x + -2x2 = 35 + 2x2 + -35 + -2x2 Reorder the terms: -11 + -2x + -2x2 = 35 + -35 + 2x2 + -2x2 Combine like terms: 35 + -35 = 0 -11 + -2x + -2x2 = 0 + 2x2 + -2x2 -11 + -2x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -11 + -2x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(11 + 2x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(11 + 2x + 2x2)' equal to zero and attempt to solve: Simplifying 11 + 2x + 2x2 = 0 Solving 11 + 2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5.5 + x + x2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + x + -5.5 + x2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + x + x2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x + x2 = 0 + -5.5 x + x2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 x + x2 = -5.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = -5.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -5.5 + 0.25 Combine like terms: -5.5 + 0.25 = -5.25 1.25 + x2 = -5.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -5.25 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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