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Simplifying 2(9x2 + 24x + 64) + -50 = 0 Reorder the terms: 2(64 + 24x + 9x2) + -50 = 0 (64 * 2 + 24x * 2 + 9x2 * 2) + -50 = 0 (128 + 48x + 18x2) + -50 = 0 Reorder the terms: 128 + -50 + 48x + 18x2 = 0 Combine like terms: 128 + -50 = 78 78 + 48x + 18x2 = 0 Solving 78 + 48x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(13 + 8x + 3x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(13 + 8x + 3x2)' equal to zero and attempt to solve: Simplifying 13 + 8x + 3x2 = 0 Solving 13 + 8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4.333333333 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '-4.333333333' to each side of the equation. 4.333333333 + 2.666666667x + -4.333333333 + x2 = 0 + -4.333333333 Reorder the terms: 4.333333333 + -4.333333333 + 2.666666667x + x2 = 0 + -4.333333333 Combine like terms: 4.333333333 + -4.333333333 = 0.000000000 0.000000000 + 2.666666667x + x2 = 0 + -4.333333333 2.666666667x + x2 = 0 + -4.333333333 Combine like terms: 0 + -4.333333333 = -4.333333333 2.666666667x + x2 = -4.333333333 The x term is 2.666666667x. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x + 1.777777780 + x2 = -4.333333333 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = -4.333333333 + 1.777777780 Combine like terms: -4.333333333 + 1.777777780 = -2.555555553 1.777777780 + 2.666666667x + x2 = -2.555555553 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = -2.555555553 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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