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Simplifying 360 = x(x + -3) + (x + 8) + (x + -5) Reorder the terms: 360 = x(-3 + x) + (x + 8) + (x + -5) 360 = (-3 * x + x * x) + (x + 8) + (x + -5) 360 = (-3x + x2) + (x + 8) + (x + -5) Reorder the terms: 360 = -3x + x2 + (8 + x) + (x + -5) Remove parenthesis around (8 + x) 360 = -3x + x2 + 8 + x + (x + -5) Reorder the terms: 360 = -3x + x2 + 8 + x + (-5 + x) Remove parenthesis around (-5 + x) 360 = -3x + x2 + 8 + x + -5 + x Reorder the terms: 360 = 8 + -5 + -3x + x + x + x2 Combine like terms: 8 + -5 = 3 360 = 3 + -3x + x + x + x2 Combine like terms: -3x + x = -2x 360 = 3 + -2x + x + x2 Combine like terms: -2x + x = -1x 360 = 3 + -1x + x2 Solving 360 = 3 + -1x + x2 Solving for variable 'x'. Combine like terms: 360 + -3 = 357 357 + x + -1x2 = 3 + -1x + x2 + -3 + x + -1x2 Reorder the terms: 357 + x + -1x2 = 3 + -3 + -1x + x + x2 + -1x2 Combine like terms: 3 + -3 = 0 357 + x + -1x2 = 0 + -1x + x + x2 + -1x2 357 + x + -1x2 = -1x + x + x2 + -1x2 Combine like terms: -1x + x = 0 357 + x + -1x2 = 0 + x2 + -1x2 357 + x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 357 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -357 + -1x + x2 = 0 Move the constant term to the right: Add '357' to each side of the equation. -357 + -1x + 357 + x2 = 0 + 357 Reorder the terms: -357 + 357 + -1x + x2 = 0 + 357 Combine like terms: -357 + 357 = 0 0 + -1x + x2 = 0 + 357 -1x + x2 = 0 + 357 Combine like terms: 0 + 357 = 357 -1x + x2 = 357 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. -1x + 0.25 + x2 = 357 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 357 + 0.25 Combine like terms: 357 + 0.25 = 357.25 0.25 + -1x + x2 = 357.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 357.25 Calculate the square root of the right side: 18.901058171 Break this problem into two subproblems by setting (x + 0.5) equal to 18.901058171 and -18.901058171.Subproblem 1
x + 0.5 = 18.901058171 Simplifying x + 0.5 = 18.901058171 Reorder the terms: 0.5 + x = 18.901058171 Solving 0.5 + x = 18.901058171 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 = 18.901058171 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 18.901058171 + -0.5 x = 18.901058171 + -0.5 Combine like terms: 18.901058171 + -0.5 = 18.401058171 x = 18.401058171 Simplifying x = 18.401058171Subproblem 2
x + 0.5 = -18.901058171 Simplifying x + 0.5 = -18.901058171 Reorder the terms: 0.5 + x = -18.901058171 Solving 0.5 + x = -18.901058171 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 = -18.901058171 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -18.901058171 + -0.5 x = -18.901058171 + -0.5 Combine like terms: -18.901058171 + -0.5 = -19.401058171 x = -19.401058171 Simplifying x = -19.401058171Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.401058171, -19.401058171}
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