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Simplifying 0 = 13x2 + 8x + 236 Reorder the terms: 0 = 236 + 8x + 13x2 Solving 0 = 236 + 8x + 13x2 Solving for variable 'x'. Combine like terms: 0 + -236 = -236 -236 + -8x + -13x2 = 236 + 8x + 13x2 + -236 + -8x + -13x2 Reorder the terms: -236 + -8x + -13x2 = 236 + -236 + 8x + -8x + 13x2 + -13x2 Combine like terms: 236 + -236 = 0 -236 + -8x + -13x2 = 0 + 8x + -8x + 13x2 + -13x2 -236 + -8x + -13x2 = 8x + -8x + 13x2 + -13x2 Combine like terms: 8x + -8x = 0 -236 + -8x + -13x2 = 0 + 13x2 + -13x2 -236 + -8x + -13x2 = 13x2 + -13x2 Combine like terms: 13x2 + -13x2 = 0 -236 + -8x + -13x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(236 + 8x + 13x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(236 + 8x + 13x2)' equal to zero and attempt to solve: Simplifying 236 + 8x + 13x2 = 0 Solving 236 + 8x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 18.15384615 + 0.6153846154x + x2 = 0 Move the constant term to the right: Add '-18.15384615' to each side of the equation. 18.15384615 + 0.6153846154x + -18.15384615 + x2 = 0 + -18.15384615 Reorder the terms: 18.15384615 + -18.15384615 + 0.6153846154x + x2 = 0 + -18.15384615 Combine like terms: 18.15384615 + -18.15384615 = 0.00000000 0.00000000 + 0.6153846154x + x2 = 0 + -18.15384615 0.6153846154x + x2 = 0 + -18.15384615 Combine like terms: 0 + -18.15384615 = -18.15384615 0.6153846154x + x2 = -18.15384615 The x term is 0.6153846154x. Take half its coefficient (0.3076923077). Square it (0.09467455622) and add it to both sides. Add '0.09467455622' to each side of the equation. 0.6153846154x + 0.09467455622 + x2 = -18.15384615 + 0.09467455622 Reorder the terms: 0.09467455622 + 0.6153846154x + x2 = -18.15384615 + 0.09467455622 Combine like terms: -18.15384615 + 0.09467455622 = -18.05917159378 0.09467455622 + 0.6153846154x + x2 = -18.05917159378 Factor a perfect square on the left side: (x + 0.3076923077)(x + 0.3076923077) = -18.05917159378 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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