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Simplifying -0.0384x2 + 1.7664x + -1.31 = 0 Reorder the terms: -1.31 + 1.7664x + -0.0384x2 = 0 Solving -1.31 + 1.7664x + -0.0384x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.0384 the coefficient of the squared term: Divide each side by '-0.0384'. 34.11458333 + -46x + x2 = 0 Move the constant term to the right: Add '-34.11458333' to each side of the equation. 34.11458333 + -46x + -34.11458333 + x2 = 0 + -34.11458333 Reorder the terms: 34.11458333 + -34.11458333 + -46x + x2 = 0 + -34.11458333 Combine like terms: 34.11458333 + -34.11458333 = 0.00000000 0.00000000 + -46x + x2 = 0 + -34.11458333 -46x + x2 = 0 + -34.11458333 Combine like terms: 0 + -34.11458333 = -34.11458333 -46x + x2 = -34.11458333 The x term is -46x. Take half its coefficient (-23). Square it (529) and add it to both sides. Add '529' to each side of the equation. -46x + 529 + x2 = -34.11458333 + 529 Reorder the terms: 529 + -46x + x2 = -34.11458333 + 529 Combine like terms: -34.11458333 + 529 = 494.88541667 529 + -46x + x2 = 494.88541667 Factor a perfect square on the left side: (x + -23)(x + -23) = 494.88541667 Calculate the square root of the right side: 22.246020243 Break this problem into two subproblems by setting (x + -23) equal to 22.246020243 and -22.246020243.Subproblem 1
x + -23 = 22.246020243 Simplifying x + -23 = 22.246020243 Reorder the terms: -23 + x = 22.246020243 Solving -23 + x = 22.246020243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + x = 22.246020243 + 23 Combine like terms: -23 + 23 = 0 0 + x = 22.246020243 + 23 x = 22.246020243 + 23 Combine like terms: 22.246020243 + 23 = 45.246020243 x = 45.246020243 Simplifying x = 45.246020243Subproblem 2
x + -23 = -22.246020243 Simplifying x + -23 = -22.246020243 Reorder the terms: -23 + x = -22.246020243 Solving -23 + x = -22.246020243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + x = -22.246020243 + 23 Combine like terms: -23 + 23 = 0 0 + x = -22.246020243 + 23 x = -22.246020243 + 23 Combine like terms: -22.246020243 + 23 = 0.753979757 x = 0.753979757 Simplifying x = 0.753979757Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.246020243, 0.753979757}
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