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Simplifying 4x2 + -37x + 18 = 0 Reorder the terms: 18 + -37x + 4x2 = 0 Solving 18 + -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'. 4.5 + -9.25x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -9.25x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -9.25x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -9.25x + x2 = 0 + -4.5 -9.25x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -9.25x + x2 = -4.5 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 = -4.5 + 21.390625 Reorder the terms: 21.390625 + -9.25x + x2 = -4.5 + 21.390625 Combine like terms: -4.5 + 21.390625 = 16.890625 21.390625 + -9.25x + x2 = 16.890625 Factor a perfect square on the left side: (x + -4.625)(x + -4.625) = 16.890625 Calculate the square root of the right side: 4.109820556 Break this problem into two subproblems by setting (x + -4.625) equal to 4.109820556 and -4.109820556.Subproblem 1
x + -4.625 = 4.109820556 Simplifying x + -4.625 = 4.109820556 Reorder the terms: -4.625 + x = 4.109820556 Solving -4.625 + x = 4.109820556 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 = 4.109820556 + 4.625 Combine like terms: -4.625 + 4.625 = 0.000 0.000 + x = 4.109820556 + 4.625 x = 4.109820556 + 4.625 Combine like terms: 4.109820556 + 4.625 = 8.734820556 x = 8.734820556 Simplifying x = 8.734820556Subproblem 2
x + -4.625 = -4.109820556 Simplifying x + -4.625 = -4.109820556 Reorder the terms: -4.625 + x = -4.109820556 Solving -4.625 + x = -4.109820556 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 = -4.109820556 + 4.625 Combine like terms: -4.625 + 4.625 = 0.000 0.000 + x = -4.109820556 + 4.625 x = -4.109820556 + 4.625 Combine like terms: -4.109820556 + 4.625 = 0.515179444 x = 0.515179444 Simplifying x = 0.515179444Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.734820556, 0.515179444}
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