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Simplifying 104 = 0.5[(360 + -1x) * x] Reorder the terms for easier multiplication: 104 = 0.5[x(360 + -1x)] 104 = 0.5[(360 * x + -1x * x)] 104 = 0.5[(360x + -1x2)] 104 = [360x * 0.5 + -1x2 * 0.5] 104 = [180x + -0.5x2] Solving 104 = 180x + -0.5x2 Solving for variable 'x'. Reorder the terms: 104 + -180x + 0.5x2 = 180x + -180x + -0.5x2 + 0.5x2 Combine like terms: 180x + -180x = 0 104 + -180x + 0.5x2 = 0 + -0.5x2 + 0.5x2 104 + -180x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 104 + -180x + 0.5x2 = 0.0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 208 + -360x + x2 = 0 Move the constant term to the right: Add '-208' to each side of the equation. 208 + -360x + -208 + x2 = 0 + -208 Reorder the terms: 208 + -208 + -360x + x2 = 0 + -208 Combine like terms: 208 + -208 = 0 0 + -360x + x2 = 0 + -208 -360x + x2 = 0 + -208 Combine like terms: 0 + -208 = -208 -360x + x2 = -208 The x term is -360x. Take half its coefficient (-180). Square it (32400) and add it to both sides. Add '32400' to each side of the equation. -360x + 32400 + x2 = -208 + 32400 Reorder the terms: 32400 + -360x + x2 = -208 + 32400 Combine like terms: -208 + 32400 = 32192 32400 + -360x + x2 = 32192 Factor a perfect square on the left side: (x + -180)(x + -180) = 32192 Calculate the square root of the right side: 179.421291936 Break this problem into two subproblems by setting (x + -180) equal to 179.421291936 and -179.421291936.Subproblem 1
x + -180 = 179.421291936 Simplifying x + -180 = 179.421291936 Reorder the terms: -180 + x = 179.421291936 Solving -180 + x = 179.421291936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '180' to each side of the equation. -180 + 180 + x = 179.421291936 + 180 Combine like terms: -180 + 180 = 0 0 + x = 179.421291936 + 180 x = 179.421291936 + 180 Combine like terms: 179.421291936 + 180 = 359.421291936 x = 359.421291936 Simplifying x = 359.421291936Subproblem 2
x + -180 = -179.421291936 Simplifying x + -180 = -179.421291936 Reorder the terms: -180 + x = -179.421291936 Solving -180 + x = -179.421291936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '180' to each side of the equation. -180 + 180 + x = -179.421291936 + 180 Combine like terms: -180 + 180 = 0 0 + x = -179.421291936 + 180 x = -179.421291936 + 180 Combine like terms: -179.421291936 + 180 = 0.578708064 x = 0.578708064 Simplifying x = 0.578708064Solution
The solution to the problem is based on the solutions from the subproblems. x = {359.421291936, 0.578708064}
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