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Simplifying 52x2 + 32x + 20 = 0 Reorder the terms: 20 + 32x + 52x2 = 0 Solving 20 + 32x + 52x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(5 + 8x + 13x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + 8x + 13x2)' equal to zero and attempt to solve: Simplifying 5 + 8x + 13x2 = 0 Solving 5 + 8x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 0.3846153846 + 0.6153846154x + x2 = 0 Move the constant term to the right: Add '-0.3846153846' to each side of the equation. 0.3846153846 + 0.6153846154x + -0.3846153846 + x2 = 0 + -0.3846153846 Reorder the terms: 0.3846153846 + -0.3846153846 + 0.6153846154x + x2 = 0 + -0.3846153846 Combine like terms: 0.3846153846 + -0.3846153846 = 0.0000000000 0.0000000000 + 0.6153846154x + x2 = 0 + -0.3846153846 0.6153846154x + x2 = 0 + -0.3846153846 Combine like terms: 0 + -0.3846153846 = -0.3846153846 0.6153846154x + x2 = -0.3846153846 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 = -0.3846153846 + 0.09467455622 Reorder the terms: 0.09467455622 + 0.6153846154x + x2 = -0.3846153846 + 0.09467455622 Combine like terms: -0.3846153846 + 0.09467455622 = -0.28994082838 0.09467455622 + 0.6153846154x + x2 = -0.28994082838 Factor a perfect square on the left side: (x + 0.3076923077)(x + 0.3076923077) = -0.28994082838 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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