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Simplifying 4x(x + -2) = 10x + -40 Reorder the terms: 4x(-2 + x) = 10x + -40 (-2 * 4x + x * 4x) = 10x + -40 (-8x + 4x2) = 10x + -40 Reorder the terms: -8x + 4x2 = -40 + 10x Solving -8x + 4x2 = -40 + 10x Solving for variable 'x'. Reorder the terms: 40 + -8x + -10x + 4x2 = -40 + 10x + 40 + -10x Combine like terms: -8x + -10x = -18x 40 + -18x + 4x2 = -40 + 10x + 40 + -10x Reorder the terms: 40 + -18x + 4x2 = -40 + 40 + 10x + -10x Combine like terms: -40 + 40 = 0 40 + -18x + 4x2 = 0 + 10x + -10x 40 + -18x + 4x2 = 10x + -10x Combine like terms: 10x + -10x = 0 40 + -18x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(20 + -9x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(20 + -9x + 2x2)' equal to zero and attempt to solve: Simplifying 20 + -9x + 2x2 = 0 Solving 20 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 10 + -4.5x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -4.5x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -4.5x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -4.5x + x2 = 0 + -10 -4.5x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -4.5x + x2 = -10 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = -10 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -10 + 5.0625 Combine like terms: -10 + 5.0625 = -4.9375 5.0625 + -4.5x + x2 = -4.9375 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = -4.9375 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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