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Simplifying 100x2 + -20x + 100 = 34 + -100x Reorder the terms: 100 + -20x + 100x2 = 34 + -100x Solving 100 + -20x + 100x2 = 34 + -100x Solving for variable 'x'. Reorder the terms: 100 + -34 + -20x + 100x + 100x2 = 34 + -100x + -34 + 100x Combine like terms: 100 + -34 = 66 66 + -20x + 100x + 100x2 = 34 + -100x + -34 + 100x Combine like terms: -20x + 100x = 80x 66 + 80x + 100x2 = 34 + -100x + -34 + 100x Reorder the terms: 66 + 80x + 100x2 = 34 + -34 + -100x + 100x Combine like terms: 34 + -34 = 0 66 + 80x + 100x2 = 0 + -100x + 100x 66 + 80x + 100x2 = -100x + 100x Combine like terms: -100x + 100x = 0 66 + 80x + 100x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(33 + 40x + 50x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(33 + 40x + 50x2)' equal to zero and attempt to solve: Simplifying 33 + 40x + 50x2 = 0 Solving 33 + 40x + 50x2 = 0 Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. 0.66 + 0.8x + x2 = 0.0 Move the constant term to the right: Add '-0.66' to each side of the equation. 0.66 + 0.8x + -0.66 + x2 = 0.0 + -0.66 Reorder the terms: 0.66 + -0.66 + 0.8x + x2 = 0.0 + -0.66 Combine like terms: 0.66 + -0.66 = 0.00 0.00 + 0.8x + x2 = 0.0 + -0.66 0.8x + x2 = 0.0 + -0.66 Combine like terms: 0.0 + -0.66 = -0.66 0.8x + x2 = -0.66 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = -0.66 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = -0.66 + 0.16 Combine like terms: -0.66 + 0.16 = -0.5 0.16 + 0.8x + x2 = -0.5 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = -0.5 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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