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Simplifying -16x2 = 20x2 + 24x + 5 Reorder the terms: -16x2 = 5 + 24x + 20x2 Solving -16x2 = 5 + 24x + 20x2 Solving for variable 'x'. Reorder the terms: -5 + -24x + -16x2 + -20x2 = 5 + 24x + 20x2 + -5 + -24x + -20x2 Combine like terms: -16x2 + -20x2 = -36x2 -5 + -24x + -36x2 = 5 + 24x + 20x2 + -5 + -24x + -20x2 Reorder the terms: -5 + -24x + -36x2 = 5 + -5 + 24x + -24x + 20x2 + -20x2 Combine like terms: 5 + -5 = 0 -5 + -24x + -36x2 = 0 + 24x + -24x + 20x2 + -20x2 -5 + -24x + -36x2 = 24x + -24x + 20x2 + -20x2 Combine like terms: 24x + -24x = 0 -5 + -24x + -36x2 = 0 + 20x2 + -20x2 -5 + -24x + -36x2 = 20x2 + -20x2 Combine like terms: 20x2 + -20x2 = 0 -5 + -24x + -36x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 24x + 36x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 24x + 36x2)' equal to zero and attempt to solve: Simplifying 5 + 24x + 36x2 = 0 Solving 5 + 24x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. 0.1388888889 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '-0.1388888889' to each side of the equation. 0.1388888889 + 0.6666666667x + -0.1388888889 + x2 = 0 + -0.1388888889 Reorder the terms: 0.1388888889 + -0.1388888889 + 0.6666666667x + x2 = 0 + -0.1388888889 Combine like terms: 0.1388888889 + -0.1388888889 = 0.0000000000 0.0000000000 + 0.6666666667x + x2 = 0 + -0.1388888889 0.6666666667x + x2 = 0 + -0.1388888889 Combine like terms: 0 + -0.1388888889 = -0.1388888889 0.6666666667x + x2 = -0.1388888889 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = -0.1388888889 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = -0.1388888889 + 0.1111111112 Combine like terms: -0.1388888889 + 0.1111111112 = -0.0277777777 0.1111111112 + 0.6666666667x + x2 = -0.0277777777 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = -0.0277777777 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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