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Simplifying (2x + -4)(5x + 4) = -20 Reorder the terms: (-4 + 2x)(5x + 4) = -20 Reorder the terms: (-4 + 2x)(4 + 5x) = -20 Multiply (-4 + 2x) * (4 + 5x) (-4(4 + 5x) + 2x * (4 + 5x)) = -20 ((4 * -4 + 5x * -4) + 2x * (4 + 5x)) = -20 ((-16 + -20x) + 2x * (4 + 5x)) = -20 (-16 + -20x + (4 * 2x + 5x * 2x)) = -20 (-16 + -20x + (8x + 10x2)) = -20 Combine like terms: -20x + 8x = -12x (-16 + -12x + 10x2) = -20 Solving -16 + -12x + 10x2 = -20 Solving for variable 'x'. Reorder the terms: -16 + 20 + -12x + 10x2 = -20 + 20 Combine like terms: -16 + 20 = 4 4 + -12x + 10x2 = -20 + 20 Combine like terms: -20 + 20 = 0 4 + -12x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -6x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -6x + 5x2)' equal to zero and attempt to solve: Simplifying 2 + -6x + 5x2 = 0 Solving 2 + -6x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + -1.2x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -1.2x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -1.2x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -1.2x + x2 = 0 + -0.4 -1.2x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -1.2x + x2 = -0.4 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = -0.4 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = -0.4 + 0.36 Combine like terms: -0.4 + 0.36 = -0.04 0.36 + -1.2x + x2 = -0.04 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = -0.04 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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