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Simplifying x2 + x + -328 = 0 Reorder the terms: -328 + x + x2 = 0 Solving -328 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '328' to each side of the equation. -328 + x + 328 + x2 = 0 + 328 Reorder the terms: -328 + 328 + x + x2 = 0 + 328 Combine like terms: -328 + 328 = 0 0 + x + x2 = 0 + 328 x + x2 = 0 + 328 Combine like terms: 0 + 328 = 328 x + x2 = 328 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 = 328 + 0.25 Reorder the terms: 0.25 + x + x2 = 328 + 0.25 Combine like terms: 328 + 0.25 = 328.25 0.25 + x + x2 = 328.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 328.25 Calculate the square root of the right side: 18.117670932 Break this problem into two subproblems by setting (x + 0.5) equal to 18.117670932 and -18.117670932.Subproblem 1
x + 0.5 = 18.117670932 Simplifying x + 0.5 = 18.117670932 Reorder the terms: 0.5 + x = 18.117670932 Solving 0.5 + x = 18.117670932 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 = 18.117670932 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 18.117670932 + -0.5 x = 18.117670932 + -0.5 Combine like terms: 18.117670932 + -0.5 = 17.617670932 x = 17.617670932 Simplifying x = 17.617670932Subproblem 2
x + 0.5 = -18.117670932 Simplifying x + 0.5 = -18.117670932 Reorder the terms: 0.5 + x = -18.117670932 Solving 0.5 + x = -18.117670932 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 = -18.117670932 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -18.117670932 + -0.5 x = -18.117670932 + -0.5 Combine like terms: -18.117670932 + -0.5 = -18.617670932 x = -18.617670932 Simplifying x = -18.617670932Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.617670932, -18.617670932}
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