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Simplifying x2 + 5x + -247 = 12 Reorder the terms: -247 + 5x + x2 = 12 Solving -247 + 5x + x2 = 12 Solving for variable 'x'. Reorder the terms: -247 + -12 + 5x + x2 = 12 + -12 Combine like terms: -247 + -12 = -259 -259 + 5x + x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -259 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '259' to each side of the equation. -259 + 5x + 259 + x2 = 0 + 259 Reorder the terms: -259 + 259 + 5x + x2 = 0 + 259 Combine like terms: -259 + 259 = 0 0 + 5x + x2 = 0 + 259 5x + x2 = 0 + 259 Combine like terms: 0 + 259 = 259 5x + x2 = 259 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 259 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 259 + 6.25 Combine like terms: 259 + 6.25 = 265.25 6.25 + 5x + x2 = 265.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 265.25 Calculate the square root of the right side: 16.286497475 Break this problem into two subproblems by setting (x + 2.5) equal to 16.286497475 and -16.286497475.Subproblem 1
x + 2.5 = 16.286497475 Simplifying x + 2.5 = 16.286497475 Reorder the terms: 2.5 + x = 16.286497475 Solving 2.5 + x = 16.286497475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 16.286497475 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 16.286497475 + -2.5 x = 16.286497475 + -2.5 Combine like terms: 16.286497475 + -2.5 = 13.786497475 x = 13.786497475 Simplifying x = 13.786497475Subproblem 2
x + 2.5 = -16.286497475 Simplifying x + 2.5 = -16.286497475 Reorder the terms: 2.5 + x = -16.286497475 Solving 2.5 + x = -16.286497475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -16.286497475 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -16.286497475 + -2.5 x = -16.286497475 + -2.5 Combine like terms: -16.286497475 + -2.5 = -18.786497475 x = -18.786497475 Simplifying x = -18.786497475Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.786497475, -18.786497475}
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