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Simplifying 25x2 + 686x + -2183 = 0 Reorder the terms: -2183 + 686x + 25x2 = 0 Solving -2183 + 686x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -87.32 + 27.44x + x2 = 0 Move the constant term to the right: Add '87.32' to each side of the equation. -87.32 + 27.44x + 87.32 + x2 = 0 + 87.32 Reorder the terms: -87.32 + 87.32 + 27.44x + x2 = 0 + 87.32 Combine like terms: -87.32 + 87.32 = 0.00 0.00 + 27.44x + x2 = 0 + 87.32 27.44x + x2 = 0 + 87.32 Combine like terms: 0 + 87.32 = 87.32 27.44x + x2 = 87.32 The x term is 27.44x. Take half its coefficient (13.72). Square it (188.2384) and add it to both sides. Add '188.2384' to each side of the equation. 27.44x + 188.2384 + x2 = 87.32 + 188.2384 Reorder the terms: 188.2384 + 27.44x + x2 = 87.32 + 188.2384 Combine like terms: 87.32 + 188.2384 = 275.5584 188.2384 + 27.44x + x2 = 275.5584 Factor a perfect square on the left side: (x + 13.72)(x + 13.72) = 275.5584 Calculate the square root of the right side: 16.599951807 Break this problem into two subproblems by setting (x + 13.72) equal to 16.599951807 and -16.599951807.Subproblem 1
x + 13.72 = 16.599951807 Simplifying x + 13.72 = 16.599951807 Reorder the terms: 13.72 + x = 16.599951807 Solving 13.72 + x = 16.599951807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.72' to each side of the equation. 13.72 + -13.72 + x = 16.599951807 + -13.72 Combine like terms: 13.72 + -13.72 = 0.00 0.00 + x = 16.599951807 + -13.72 x = 16.599951807 + -13.72 Combine like terms: 16.599951807 + -13.72 = 2.879951807 x = 2.879951807 Simplifying x = 2.879951807Subproblem 2
x + 13.72 = -16.599951807 Simplifying x + 13.72 = -16.599951807 Reorder the terms: 13.72 + x = -16.599951807 Solving 13.72 + x = -16.599951807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.72' to each side of the equation. 13.72 + -13.72 + x = -16.599951807 + -13.72 Combine like terms: 13.72 + -13.72 = 0.00 0.00 + x = -16.599951807 + -13.72 x = -16.599951807 + -13.72 Combine like terms: -16.599951807 + -13.72 = -30.319951807 x = -30.319951807 Simplifying x = -30.319951807Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.879951807, -30.319951807}
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