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Simplifying (2x + -1)(5x + -4) = -3x Reorder the terms: (-1 + 2x)(5x + -4) = -3x Reorder the terms: (-1 + 2x)(-4 + 5x) = -3x Multiply (-1 + 2x) * (-4 + 5x) (-1(-4 + 5x) + 2x * (-4 + 5x)) = -3x ((-4 * -1 + 5x * -1) + 2x * (-4 + 5x)) = -3x ((4 + -5x) + 2x * (-4 + 5x)) = -3x (4 + -5x + (-4 * 2x + 5x * 2x)) = -3x (4 + -5x + (-8x + 10x2)) = -3x Combine like terms: -5x + -8x = -13x (4 + -13x + 10x2) = -3x Solving 4 + -13x + 10x2 = -3x Solving for variable 'x'. Reorder the terms: 4 + -13x + 3x + 10x2 = -3x + 3x Combine like terms: -13x + 3x = -10x 4 + -10x + 10x2 = -3x + 3x Combine like terms: -3x + 3x = 0 4 + -10x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -5x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -5x + 5x2)' equal to zero and attempt to solve: Simplifying 2 + -5x + 5x2 = 0 Solving 2 + -5x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + -1x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -1x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -1x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -1x + x2 = 0 + -0.4 -1x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -1x + x2 = -0.4 The x term is -1x. 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. -1x + 0.25 + x2 = -0.4 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.4 + 0.25 Combine like terms: -0.4 + 0.25 = -0.15 0.25 + -1x + x2 = -0.15 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -0.15 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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