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Simplifying 33 = 3(10x + -5) * 2(3x + -10x) Reorder the terms: 33 = 3(-5 + 10x) * 2(3x + -10x) Combine like terms: 3x + -10x = -7x 33 = 3(-5 + 10x) * 2(-7x) Remove parenthesis around (-7x) 33 = 3(-5 + 10x) * 2 * -7x Reorder the terms for easier multiplication: 33 = 3 * 2 * -7x(-5 + 10x) Multiply 3 * 2 33 = 6 * -7x(-5 + 10x) Multiply 6 * -7 33 = -42x(-5 + 10x) 33 = (-5 * -42x + 10x * -42x) 33 = (210x + -420x2) Solving 33 = 210x + -420x2 Solving for variable 'x'. Reorder the terms: 33 + -210x + 420x2 = 210x + -210x + -420x2 + 420x2 Combine like terms: 210x + -210x = 0 33 + -210x + 420x2 = 0 + -420x2 + 420x2 33 + -210x + 420x2 = -420x2 + 420x2 Combine like terms: -420x2 + 420x2 = 0 33 + -210x + 420x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(11 + -70x + 140x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(11 + -70x + 140x2)' equal to zero and attempt to solve: Simplifying 11 + -70x + 140x2 = 0 Solving 11 + -70x + 140x2 = 0 Begin completing the square. Divide all terms by 140 the coefficient of the squared term: Divide each side by '140'. 0.07857142857 + -0.5x + x2 = 0.0 Move the constant term to the right: Add '-0.07857142857' to each side of the equation. 0.07857142857 + -0.5x + -0.07857142857 + x2 = 0.0 + -0.07857142857 Reorder the terms: 0.07857142857 + -0.07857142857 + -0.5x + x2 = 0.0 + -0.07857142857 Combine like terms: 0.07857142857 + -0.07857142857 = 0.00000000000 0.00000000000 + -0.5x + x2 = 0.0 + -0.07857142857 -0.5x + x2 = 0.0 + -0.07857142857 Combine like terms: 0.0 + -0.07857142857 = -0.07857142857 -0.5x + x2 = -0.07857142857 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = -0.07857142857 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = -0.07857142857 + 0.0625 Combine like terms: -0.07857142857 + 0.0625 = -0.01607142857 0.0625 + -0.5x + x2 = -0.01607142857 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = -0.01607142857 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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