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Simplifying 2(5x + -10) + -8(7 + -2x) + 6(-8x + 5) = -10x(8 + -7x) Reorder the terms: 2(-10 + 5x) + -8(7 + -2x) + 6(-8x + 5) = -10x(8 + -7x) (-10 * 2 + 5x * 2) + -8(7 + -2x) + 6(-8x + 5) = -10x(8 + -7x) (-20 + 10x) + -8(7 + -2x) + 6(-8x + 5) = -10x(8 + -7x) -20 + 10x + (7 * -8 + -2x * -8) + 6(-8x + 5) = -10x(8 + -7x) -20 + 10x + (-56 + 16x) + 6(-8x + 5) = -10x(8 + -7x) Reorder the terms: -20 + 10x + -56 + 16x + 6(5 + -8x) = -10x(8 + -7x) -20 + 10x + -56 + 16x + (5 * 6 + -8x * 6) = -10x(8 + -7x) -20 + 10x + -56 + 16x + (30 + -48x) = -10x(8 + -7x) Reorder the terms: -20 + -56 + 30 + 10x + 16x + -48x = -10x(8 + -7x) Combine like terms: -20 + -56 = -76 -76 + 30 + 10x + 16x + -48x = -10x(8 + -7x) Combine like terms: -76 + 30 = -46 -46 + 10x + 16x + -48x = -10x(8 + -7x) Combine like terms: 10x + 16x = 26x -46 + 26x + -48x = -10x(8 + -7x) Combine like terms: 26x + -48x = -22x -46 + -22x = -10x(8 + -7x) -46 + -22x = (8 * -10x + -7x * -10x) -46 + -22x = (-80x + 70x2) Solving -46 + -22x = -80x + 70x2 Solving for variable 'x'. Combine like terms: -22x + 80x = 58x -46 + 58x + -70x2 = -80x + 70x2 + 80x + -70x2 Reorder the terms: -46 + 58x + -70x2 = -80x + 80x + 70x2 + -70x2 Combine like terms: -80x + 80x = 0 -46 + 58x + -70x2 = 0 + 70x2 + -70x2 -46 + 58x + -70x2 = 70x2 + -70x2 Combine like terms: 70x2 + -70x2 = 0 -46 + 58x + -70x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-23 + 29x + -35x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-23 + 29x + -35x2)' equal to zero and attempt to solve: Simplifying -23 + 29x + -35x2 = 0 Solving -23 + 29x + -35x2 = 0 Begin completing the square. Divide all terms by -35 the coefficient of the squared term: Divide each side by '-35'. 0.6571428571 + -0.8285714286x + x2 = 0 Move the constant term to the right: Add '-0.6571428571' to each side of the equation. 0.6571428571 + -0.8285714286x + -0.6571428571 + x2 = 0 + -0.6571428571 Reorder the terms: 0.6571428571 + -0.6571428571 + -0.8285714286x + x2 = 0 + -0.6571428571 Combine like terms: 0.6571428571 + -0.6571428571 = 0.0000000000 0.0000000000 + -0.8285714286x + x2 = 0 + -0.6571428571 -0.8285714286x + x2 = 0 + -0.6571428571 Combine like terms: 0 + -0.6571428571 = -0.6571428571 -0.8285714286x + x2 = -0.6571428571 The x term is -0.8285714286x. Take half its coefficient (-0.4142857143). Square it (0.1716326531) and add it to both sides. Add '0.1716326531' to each side of the equation. -0.8285714286x + 0.1716326531 + x2 = -0.6571428571 + 0.1716326531 Reorder the terms: 0.1716326531 + -0.8285714286x + x2 = -0.6571428571 + 0.1716326531 Combine like terms: -0.6571428571 + 0.1716326531 = -0.485510204 0.1716326531 + -0.8285714286x + x2 = -0.485510204 Factor a perfect square on the left side: (x + -0.4142857143)(x + -0.4142857143) = -0.485510204 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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