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Simplifying -6x(-7x + -13) = -58 Reorder the terms: -6x(-13 + -7x) = -58 (-13 * -6x + -7x * -6x) = -58 (78x + 42x2) = -58 Solving 78x + 42x2 = -58 Solving for variable 'x'. Reorder the terms: 58 + 78x + 42x2 = -58 + 58 Combine like terms: -58 + 58 = 0 58 + 78x + 42x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(29 + 39x + 21x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(29 + 39x + 21x2)' equal to zero and attempt to solve: Simplifying 29 + 39x + 21x2 = 0 Solving 29 + 39x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 1.380952381 + 1.857142857x + x2 = 0 Move the constant term to the right: Add '-1.380952381' to each side of the equation. 1.380952381 + 1.857142857x + -1.380952381 + x2 = 0 + -1.380952381 Reorder the terms: 1.380952381 + -1.380952381 + 1.857142857x + x2 = 0 + -1.380952381 Combine like terms: 1.380952381 + -1.380952381 = 0.000000000 0.000000000 + 1.857142857x + x2 = 0 + -1.380952381 1.857142857x + x2 = 0 + -1.380952381 Combine like terms: 0 + -1.380952381 = -1.380952381 1.857142857x + x2 = -1.380952381 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 = -1.380952381 + 0.8622448978 Reorder the terms: 0.8622448978 + 1.857142857x + x2 = -1.380952381 + 0.8622448978 Combine like terms: -1.380952381 + 0.8622448978 = -0.5187074832 0.8622448978 + 1.857142857x + x2 = -0.5187074832 Factor a perfect square on the left side: (x + 0.9285714285)(x + 0.9285714285) = -0.5187074832 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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