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Simplifying x2 + x + -350 = 0 Reorder the terms: -350 + x + x2 = 0 Solving -350 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '350' to each side of the equation. -350 + x + 350 + x2 = 0 + 350 Reorder the terms: -350 + 350 + x + x2 = 0 + 350 Combine like terms: -350 + 350 = 0 0 + x + x2 = 0 + 350 x + x2 = 0 + 350 Combine like terms: 0 + 350 = 350 x + x2 = 350 The x term is x. 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. x + 0.25 + x2 = 350 + 0.25 Reorder the terms: 0.25 + x + x2 = 350 + 0.25 Combine like terms: 350 + 0.25 = 350.25 0.25 + x + x2 = 350.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 350.25 Calculate the square root of the right side: 18.714967272 Break this problem into two subproblems by setting (x + 0.5) equal to 18.714967272 and -18.714967272.Subproblem 1
x + 0.5 = 18.714967272 Simplifying x + 0.5 = 18.714967272 Reorder the terms: 0.5 + x = 18.714967272 Solving 0.5 + x = 18.714967272 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 = 18.714967272 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 18.714967272 + -0.5 x = 18.714967272 + -0.5 Combine like terms: 18.714967272 + -0.5 = 18.214967272 x = 18.214967272 Simplifying x = 18.214967272Subproblem 2
x + 0.5 = -18.714967272 Simplifying x + 0.5 = -18.714967272 Reorder the terms: 0.5 + x = -18.714967272 Solving 0.5 + x = -18.714967272 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 = -18.714967272 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -18.714967272 + -0.5 x = -18.714967272 + -0.5 Combine like terms: -18.714967272 + -0.5 = -19.214967272 x = -19.214967272 Simplifying x = -19.214967272Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.214967272, -19.214967272}
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