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Simplifying 5(2x + -3) * 2 + -1(5x + -2)(4x + 2) = 0 Reorder the terms: 5(-3 + 2x) * 2 + -1(5x + -2)(4x + 2) = 0 Reorder the terms for easier multiplication: 5 * 2(-3 + 2x) + -1(5x + -2)(4x + 2) = 0 Multiply 5 * 2 10(-3 + 2x) + -1(5x + -2)(4x + 2) = 0 (-3 * 10 + 2x * 10) + -1(5x + -2)(4x + 2) = 0 (-30 + 20x) + -1(5x + -2)(4x + 2) = 0 Reorder the terms: -30 + 20x + -1(-2 + 5x)(4x + 2) = 0 Reorder the terms: -30 + 20x + -1(-2 + 5x)(2 + 4x) = 0 Multiply (-2 + 5x) * (2 + 4x) -30 + 20x + -1(-2(2 + 4x) + 5x * (2 + 4x)) = 0 -30 + 20x + -1((2 * -2 + 4x * -2) + 5x * (2 + 4x)) = 0 -30 + 20x + -1((-4 + -8x) + 5x * (2 + 4x)) = 0 -30 + 20x + -1(-4 + -8x + (2 * 5x + 4x * 5x)) = 0 -30 + 20x + -1(-4 + -8x + (10x + 20x2)) = 0 Combine like terms: -8x + 10x = 2x -30 + 20x + -1(-4 + 2x + 20x2) = 0 -30 + 20x + (-4 * -1 + 2x * -1 + 20x2 * -1) = 0 -30 + 20x + (4 + -2x + -20x2) = 0 Reorder the terms: -30 + 4 + 20x + -2x + -20x2 = 0 Combine like terms: -30 + 4 = -26 -26 + 20x + -2x + -20x2 = 0 Combine like terms: 20x + -2x = 18x -26 + 18x + -20x2 = 0 Solving -26 + 18x + -20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-13 + 9x + -10x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-13 + 9x + -10x2)' equal to zero and attempt to solve: Simplifying -13 + 9x + -10x2 = 0 Solving -13 + 9x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. 1.3 + -0.9x + x2 = 0.0 Move the constant term to the right: Add '-1.3' to each side of the equation. 1.3 + -0.9x + -1.3 + x2 = 0.0 + -1.3 Reorder the terms: 1.3 + -1.3 + -0.9x + x2 = 0.0 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + -0.9x + x2 = 0.0 + -1.3 -0.9x + x2 = 0.0 + -1.3 Combine like terms: 0.0 + -1.3 = -1.3 -0.9x + x2 = -1.3 The x term is -0.9x. Take half its coefficient (-0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. -0.9x + 0.2025 + x2 = -1.3 + 0.2025 Reorder the terms: 0.2025 + -0.9x + x2 = -1.3 + 0.2025 Combine like terms: -1.3 + 0.2025 = -1.0975 0.2025 + -0.9x + x2 = -1.0975 Factor a perfect square on the left side: (x + -0.45)(x + -0.45) = -1.0975 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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