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Simplifying 0 = 4x2 + -35x + 74 Reorder the terms: 0 = 74 + -35x + 4x2 Solving 0 = 74 + -35x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -74 = -74 -74 + 35x + -4x2 = 74 + -35x + 4x2 + -74 + 35x + -4x2 Reorder the terms: -74 + 35x + -4x2 = 74 + -74 + -35x + 35x + 4x2 + -4x2 Combine like terms: 74 + -74 = 0 -74 + 35x + -4x2 = 0 + -35x + 35x + 4x2 + -4x2 -74 + 35x + -4x2 = -35x + 35x + 4x2 + -4x2 Combine like terms: -35x + 35x = 0 -74 + 35x + -4x2 = 0 + 4x2 + -4x2 -74 + 35x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -74 + 35x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 18.5 + -8.75x + x2 = 0 Move the constant term to the right: Add '-18.5' to each side of the equation. 18.5 + -8.75x + -18.5 + x2 = 0 + -18.5 Reorder the terms: 18.5 + -18.5 + -8.75x + x2 = 0 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + -8.75x + x2 = 0 + -18.5 -8.75x + x2 = 0 + -18.5 Combine like terms: 0 + -18.5 = -18.5 -8.75x + x2 = -18.5 The x term is -8.75x. Take half its coefficient (-4.375). Square it (19.140625) and add it to both sides. Add '19.140625' to each side of the equation. -8.75x + 19.140625 + x2 = -18.5 + 19.140625 Reorder the terms: 19.140625 + -8.75x + x2 = -18.5 + 19.140625 Combine like terms: -18.5 + 19.140625 = 0.640625 19.140625 + -8.75x + x2 = 0.640625 Factor a perfect square on the left side: (x + -4.375)(x + -4.375) = 0.640625 Calculate the square root of the right side: 0.80039053 Break this problem into two subproblems by setting (x + -4.375) equal to 0.80039053 and -0.80039053.Subproblem 1
x + -4.375 = 0.80039053 Simplifying x + -4.375 = 0.80039053 Reorder the terms: -4.375 + x = 0.80039053 Solving -4.375 + x = 0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + x = 0.80039053 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + x = 0.80039053 + 4.375 x = 0.80039053 + 4.375 Combine like terms: 0.80039053 + 4.375 = 5.17539053 x = 5.17539053 Simplifying x = 5.17539053Subproblem 2
x + -4.375 = -0.80039053 Simplifying x + -4.375 = -0.80039053 Reorder the terms: -4.375 + x = -0.80039053 Solving -4.375 + x = -0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + x = -0.80039053 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + x = -0.80039053 + 4.375 x = -0.80039053 + 4.375 Combine like terms: -0.80039053 + 4.375 = 3.57460947 x = 3.57460947 Simplifying x = 3.57460947Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.17539053, 3.57460947}
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