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Simplifying 4x2 + -37x + 74 = 0 Reorder the terms: 74 + -37x + 4x2 = 0 Solving 74 + -37x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 18.5 + -9.25x + x2 = 0 Move the constant term to the right: Add '-18.5' to each side of the equation. 18.5 + -9.25x + -18.5 + x2 = 0 + -18.5 Reorder the terms: 18.5 + -18.5 + -9.25x + x2 = 0 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + -9.25x + x2 = 0 + -18.5 -9.25x + x2 = 0 + -18.5 Combine like terms: 0 + -18.5 = -18.5 -9.25x + x2 = -18.5 The x term is -9.25x. Take half its coefficient (-4.625). Square it (21.390625) and add it to both sides. Add '21.390625' to each side of the equation. -9.25x + 21.390625 + x2 = -18.5 + 21.390625 Reorder the terms: 21.390625 + -9.25x + x2 = -18.5 + 21.390625 Combine like terms: -18.5 + 21.390625 = 2.890625 21.390625 + -9.25x + x2 = 2.890625 Factor a perfect square on the left side: (x + -4.625)(x + -4.625) = 2.890625 Calculate the square root of the right side: 1.700183814 Break this problem into two subproblems by setting (x + -4.625) equal to 1.700183814 and -1.700183814.Subproblem 1
x + -4.625 = 1.700183814 Simplifying x + -4.625 = 1.700183814 Reorder the terms: -4.625 + x = 1.700183814 Solving -4.625 + x = 1.700183814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.625' to each side of the equation. -4.625 + 4.625 + x = 1.700183814 + 4.625 Combine like terms: -4.625 + 4.625 = 0.000 0.000 + x = 1.700183814 + 4.625 x = 1.700183814 + 4.625 Combine like terms: 1.700183814 + 4.625 = 6.325183814 x = 6.325183814 Simplifying x = 6.325183814Subproblem 2
x + -4.625 = -1.700183814 Simplifying x + -4.625 = -1.700183814 Reorder the terms: -4.625 + x = -1.700183814 Solving -4.625 + x = -1.700183814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.625' to each side of the equation. -4.625 + 4.625 + x = -1.700183814 + 4.625 Combine like terms: -4.625 + 4.625 = 0.000 0.000 + x = -1.700183814 + 4.625 x = -1.700183814 + 4.625 Combine like terms: -1.700183814 + 4.625 = 2.924816186 x = 2.924816186 Simplifying x = 2.924816186Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.325183814, 2.924816186}
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