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Simplifying -7x2 + -29x + -34 = 0 Reorder the terms: -34 + -29x + -7x2 = 0 Solving -34 + -29x + -7x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(34 + 29x + 7x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(34 + 29x + 7x2)' equal to zero and attempt to solve: Simplifying 34 + 29x + 7x2 = 0 Solving 34 + 29x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 4.857142857 + 4.142857143x + x2 = 0 Move the constant term to the right: Add '-4.857142857' to each side of the equation. 4.857142857 + 4.142857143x + -4.857142857 + x2 = 0 + -4.857142857 Reorder the terms: 4.857142857 + -4.857142857 + 4.142857143x + x2 = 0 + -4.857142857 Combine like terms: 4.857142857 + -4.857142857 = 0.000000000 0.000000000 + 4.142857143x + x2 = 0 + -4.857142857 4.142857143x + x2 = 0 + -4.857142857 Combine like terms: 0 + -4.857142857 = -4.857142857 4.142857143x + x2 = -4.857142857 The x term is 4.142857143x. Take half its coefficient (2.071428572). Square it (4.290816329) and add it to both sides. Add '4.290816329' to each side of the equation. 4.142857143x + 4.290816329 + x2 = -4.857142857 + 4.290816329 Reorder the terms: 4.290816329 + 4.142857143x + x2 = -4.857142857 + 4.290816329 Combine like terms: -4.857142857 + 4.290816329 = -0.566326528 4.290816329 + 4.142857143x + x2 = -0.566326528 Factor a perfect square on the left side: (x + 2.071428572)(x + 2.071428572) = -0.566326528 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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