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Simplifying 13 = 3 + 5x(-2 + -2x) + 5 13 = 3 + (-2 * 5x + -2x * 5x) + 5 13 = 3 + (-10x + -10x2) + 5 Reorder the terms: 13 = 3 + 5 + -10x + -10x2 Combine like terms: 3 + 5 = 8 13 = 8 + -10x + -10x2 Solving 13 = 8 + -10x + -10x2 Solving for variable 'x'. Combine like terms: 13 + -8 = 5 5 + 10x + 10x2 = 8 + -10x + -10x2 + -8 + 10x + 10x2 Reorder the terms: 5 + 10x + 10x2 = 8 + -8 + -10x + 10x + -10x2 + 10x2 Combine like terms: 8 + -8 = 0 5 + 10x + 10x2 = 0 + -10x + 10x + -10x2 + 10x2 5 + 10x + 10x2 = -10x + 10x + -10x2 + 10x2 Combine like terms: -10x + 10x = 0 5 + 10x + 10x2 = 0 + -10x2 + 10x2 5 + 10x + 10x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 5 + 10x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(1 + 2x + 2x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + 2x + 2x2)' equal to zero and attempt to solve: Simplifying 1 + 2x + 2x2 = 0 Solving 1 + 2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x + x2 = 0 + -0.5 x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 x + x2 = -0.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = -0.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -0.5 + 0.25 Combine like terms: -0.5 + 0.25 = -0.25 1.25 + x2 = -0.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.25 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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