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Simplifying -2x2 + -7x + -29 = 0 Reorder the terms: -29 + -7x + -2x2 = 0 Solving -29 + -7x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(29 + 7x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(29 + 7x + 2x2)' equal to zero and attempt to solve: Simplifying 29 + 7x + 2x2 = 0 Solving 29 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 14.5 + 3.5x + x2 = 0 Move the constant term to the right: Add '-14.5' to each side of the equation. 14.5 + 3.5x + -14.5 + x2 = 0 + -14.5 Reorder the terms: 14.5 + -14.5 + 3.5x + x2 = 0 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + 3.5x + x2 = 0 + -14.5 3.5x + x2 = 0 + -14.5 Combine like terms: 0 + -14.5 = -14.5 3.5x + x2 = -14.5 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = -14.5 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = -14.5 + 3.0625 Combine like terms: -14.5 + 3.0625 = -11.4375 3.0625 + 3.5x + x2 = -11.4375 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = -11.4375 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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