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Simplifying -7x2 + -13x + -24 = 0 Reorder the terms: -24 + -13x + -7x2 = 0 Solving -24 + -13x + -7x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(24 + 13x + 7x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(24 + 13x + 7x2)' equal to zero and attempt to solve: Simplifying 24 + 13x + 7x2 = 0 Solving 24 + 13x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 3.428571429 + 1.857142857x + x2 = 0 Move the constant term to the right: Add '-3.428571429' to each side of the equation. 3.428571429 + 1.857142857x + -3.428571429 + x2 = 0 + -3.428571429 Reorder the terms: 3.428571429 + -3.428571429 + 1.857142857x + x2 = 0 + -3.428571429 Combine like terms: 3.428571429 + -3.428571429 = 0.000000000 0.000000000 + 1.857142857x + x2 = 0 + -3.428571429 1.857142857x + x2 = 0 + -3.428571429 Combine like terms: 0 + -3.428571429 = -3.428571429 1.857142857x + x2 = -3.428571429 The x term is 1.857142857x. Take half its coefficient (0.9285714285). Square it (0.8622448978) and add it to both sides. Add '0.8622448978' to each side of the equation. 1.857142857x + 0.8622448978 + x2 = -3.428571429 + 0.8622448978 Reorder the terms: 0.8622448978 + 1.857142857x + x2 = -3.428571429 + 0.8622448978 Combine like terms: -3.428571429 + 0.8622448978 = -2.5663265312 0.8622448978 + 1.857142857x + x2 = -2.5663265312 Factor a perfect square on the left side: (x + 0.9285714285)(x + 0.9285714285) = -2.5663265312 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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