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Simplifying x2 + -361 = x + -2 Reorder the terms: -361 + x2 = x + -2 Reorder the terms: -361 + x2 = -2 + x Solving -361 + x2 = -2 + x Solving for variable 'x'. Reorder the terms: -361 + 2 + -1x + x2 = -2 + x + 2 + -1x Combine like terms: -361 + 2 = -359 -359 + -1x + x2 = -2 + x + 2 + -1x Reorder the terms: -359 + -1x + x2 = -2 + 2 + x + -1x Combine like terms: -2 + 2 = 0 -359 + -1x + x2 = 0 + x + -1x -359 + -1x + x2 = x + -1x Combine like terms: x + -1x = 0 -359 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '359' to each side of the equation. -359 + -1x + 359 + x2 = 0 + 359 Reorder the terms: -359 + 359 + -1x + x2 = 0 + 359 Combine like terms: -359 + 359 = 0 0 + -1x + x2 = 0 + 359 -1x + x2 = 0 + 359 Combine like terms: 0 + 359 = 359 -1x + x2 = 359 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 359 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 359 + 0.25 Combine like terms: 359 + 0.25 = 359.25 0.25 + -1x + x2 = 359.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 359.25 Calculate the square root of the right side: 18.953891421 Break this problem into two subproblems by setting (x + -0.5) equal to 18.953891421 and -18.953891421.Subproblem 1
x + -0.5 = 18.953891421 Simplifying x + -0.5 = 18.953891421 Reorder the terms: -0.5 + x = 18.953891421 Solving -0.5 + x = 18.953891421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 18.953891421 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 18.953891421 + 0.5 x = 18.953891421 + 0.5 Combine like terms: 18.953891421 + 0.5 = 19.453891421 x = 19.453891421 Simplifying x = 19.453891421Subproblem 2
x + -0.5 = -18.953891421 Simplifying x + -0.5 = -18.953891421 Reorder the terms: -0.5 + x = -18.953891421 Solving -0.5 + x = -18.953891421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -18.953891421 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -18.953891421 + 0.5 x = -18.953891421 + 0.5 Combine like terms: -18.953891421 + 0.5 = -18.453891421 x = -18.453891421 Simplifying x = -18.453891421Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.453891421, -18.453891421}
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