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Simplifying 0 = x2 + -100x + 600 Reorder the terms: 0 = 600 + -100x + x2 Solving 0 = 600 + -100x + x2 Solving for variable 'x'. Combine like terms: 0 + -600 = -600 -600 + 100x + -1x2 = 600 + -100x + x2 + -600 + 100x + -1x2 Reorder the terms: -600 + 100x + -1x2 = 600 + -600 + -100x + 100x + x2 + -1x2 Combine like terms: 600 + -600 = 0 -600 + 100x + -1x2 = 0 + -100x + 100x + x2 + -1x2 -600 + 100x + -1x2 = -100x + 100x + x2 + -1x2 Combine like terms: -100x + 100x = 0 -600 + 100x + -1x2 = 0 + x2 + -1x2 -600 + 100x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -600 + 100x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 600 + -100x + x2 = 0 Move the constant term to the right: Add '-600' to each side of the equation. 600 + -100x + -600 + x2 = 0 + -600 Reorder the terms: 600 + -600 + -100x + x2 = 0 + -600 Combine like terms: 600 + -600 = 0 0 + -100x + x2 = 0 + -600 -100x + x2 = 0 + -600 Combine like terms: 0 + -600 = -600 -100x + x2 = -600 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -600 + 2500 Reorder the terms: 2500 + -100x + x2 = -600 + 2500 Combine like terms: -600 + 2500 = 1900 2500 + -100x + x2 = 1900 Factor a perfect square on the left side: (x + -50)(x + -50) = 1900 Calculate the square root of the right side: 43.588989435 Break this problem into two subproblems by setting (x + -50) equal to 43.588989435 and -43.588989435.Subproblem 1
x + -50 = 43.588989435 Simplifying x + -50 = 43.588989435 Reorder the terms: -50 + x = 43.588989435 Solving -50 + x = 43.588989435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 43.588989435 + 50 Combine like terms: -50 + 50 = 0 0 + x = 43.588989435 + 50 x = 43.588989435 + 50 Combine like terms: 43.588989435 + 50 = 93.588989435 x = 93.588989435 Simplifying x = 93.588989435Subproblem 2
x + -50 = -43.588989435 Simplifying x + -50 = -43.588989435 Reorder the terms: -50 + x = -43.588989435 Solving -50 + x = -43.588989435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -43.588989435 + 50 Combine like terms: -50 + 50 = 0 0 + x = -43.588989435 + 50 x = -43.588989435 + 50 Combine like terms: -43.588989435 + 50 = 6.411010565 x = 6.411010565 Simplifying x = 6.411010565Solution
The solution to the problem is based on the solutions from the subproblems. x = {93.588989435, 6.411010565}
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