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Simplifying (2x + -1)(5x + -4) + (5x + 4)(2x + 5) = 0 Reorder the terms: (-1 + 2x)(5x + -4) + (5x + 4)(2x + 5) = 0 Reorder the terms: (-1 + 2x)(-4 + 5x) + (5x + 4)(2x + 5) = 0 Multiply (-1 + 2x) * (-4 + 5x) (-1(-4 + 5x) + 2x * (-4 + 5x)) + (5x + 4)(2x + 5) = 0 ((-4 * -1 + 5x * -1) + 2x * (-4 + 5x)) + (5x + 4)(2x + 5) = 0 ((4 + -5x) + 2x * (-4 + 5x)) + (5x + 4)(2x + 5) = 0 (4 + -5x + (-4 * 2x + 5x * 2x)) + (5x + 4)(2x + 5) = 0 (4 + -5x + (-8x + 10x2)) + (5x + 4)(2x + 5) = 0 Combine like terms: -5x + -8x = -13x (4 + -13x + 10x2) + (5x + 4)(2x + 5) = 0 Reorder the terms: 4 + -13x + 10x2 + (4 + 5x)(2x + 5) = 0 Reorder the terms: 4 + -13x + 10x2 + (4 + 5x)(5 + 2x) = 0 Multiply (4 + 5x) * (5 + 2x) 4 + -13x + 10x2 + (4(5 + 2x) + 5x * (5 + 2x)) = 0 4 + -13x + 10x2 + ((5 * 4 + 2x * 4) + 5x * (5 + 2x)) = 0 4 + -13x + 10x2 + ((20 + 8x) + 5x * (5 + 2x)) = 0 4 + -13x + 10x2 + (20 + 8x + (5 * 5x + 2x * 5x)) = 0 4 + -13x + 10x2 + (20 + 8x + (25x + 10x2)) = 0 Combine like terms: 8x + 25x = 33x 4 + -13x + 10x2 + (20 + 33x + 10x2) = 0 Reorder the terms: 4 + 20 + -13x + 33x + 10x2 + 10x2 = 0 Combine like terms: 4 + 20 = 24 24 + -13x + 33x + 10x2 + 10x2 = 0 Combine like terms: -13x + 33x = 20x 24 + 20x + 10x2 + 10x2 = 0 Combine like terms: 10x2 + 10x2 = 20x2 24 + 20x + 20x2 = 0 Solving 24 + 20x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(6 + 5x + 5x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(6 + 5x + 5x2)' equal to zero and attempt to solve: Simplifying 6 + 5x + 5x2 = 0 Solving 6 + 5x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.2 + x + x2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + x + -1.2 + x2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + x + x2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x + x2 = 0 + -1.2 x + x2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 x + x2 = -1.2 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 = -1.2 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -1.2 + 0.25 Combine like terms: -1.2 + 0.25 = -0.95 1.25 + x2 = -0.95 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.95 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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