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Simplifying 17x2 + -600x + 600 = 0 Reorder the terms: 600 + -600x + 17x2 = 0 Solving 600 + -600x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. 35.29411765 + -35.29411765x + x2 = 0 Move the constant term to the right: Add '-35.29411765' to each side of the equation. 35.29411765 + -35.29411765x + -35.29411765 + x2 = 0 + -35.29411765 Reorder the terms: 35.29411765 + -35.29411765 + -35.29411765x + x2 = 0 + -35.29411765 Combine like terms: 35.29411765 + -35.29411765 = 0.00000000 0.00000000 + -35.29411765x + x2 = 0 + -35.29411765 -35.29411765x + x2 = 0 + -35.29411765 Combine like terms: 0 + -35.29411765 = -35.29411765 -35.29411765x + x2 = -35.29411765 The x term is -35.29411765x. Take half its coefficient (-17.64705883). Square it (311.4186853) and add it to both sides. Add '311.4186853' to each side of the equation. -35.29411765x + 311.4186853 + x2 = -35.29411765 + 311.4186853 Reorder the terms: 311.4186853 + -35.29411765x + x2 = -35.29411765 + 311.4186853 Combine like terms: -35.29411765 + 311.4186853 = 276.12456765 311.4186853 + -35.29411765x + x2 = 276.12456765 Factor a perfect square on the left side: (x + -17.64705883)(x + -17.64705883) = 276.12456765 Calculate the square root of the right side: 16.616996349 Break this problem into two subproblems by setting (x + -17.64705883) equal to 16.616996349 and -16.616996349.Subproblem 1
x + -17.64705883 = 16.616996349 Simplifying x + -17.64705883 = 16.616996349 Reorder the terms: -17.64705883 + x = 16.616996349 Solving -17.64705883 + x = 16.616996349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.64705883' to each side of the equation. -17.64705883 + 17.64705883 + x = 16.616996349 + 17.64705883 Combine like terms: -17.64705883 + 17.64705883 = 0.00000000 0.00000000 + x = 16.616996349 + 17.64705883 x = 16.616996349 + 17.64705883 Combine like terms: 16.616996349 + 17.64705883 = 34.264055179 x = 34.264055179 Simplifying x = 34.264055179Subproblem 2
x + -17.64705883 = -16.616996349 Simplifying x + -17.64705883 = -16.616996349 Reorder the terms: -17.64705883 + x = -16.616996349 Solving -17.64705883 + x = -16.616996349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.64705883' to each side of the equation. -17.64705883 + 17.64705883 + x = -16.616996349 + 17.64705883 Combine like terms: -17.64705883 + 17.64705883 = 0.00000000 0.00000000 + x = -16.616996349 + 17.64705883 x = -16.616996349 + 17.64705883 Combine like terms: -16.616996349 + 17.64705883 = 1.030062481 x = 1.030062481 Simplifying x = 1.030062481Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.264055179, 1.030062481}
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