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Simplifying -0.01x2 + 6x + -700 = 0 Reorder the terms: -700 + 6x + -0.01x2 = 0 Solving -700 + 6x + -0.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. 70000 + -600x + x2 = 0 Move the constant term to the right: Add '-70000' to each side of the equation. 70000 + -600x + -70000 + x2 = 0 + -70000 Reorder the terms: 70000 + -70000 + -600x + x2 = 0 + -70000 Combine like terms: 70000 + -70000 = 0 0 + -600x + x2 = 0 + -70000 -600x + x2 = 0 + -70000 Combine like terms: 0 + -70000 = -70000 -600x + x2 = -70000 The x term is -600x. Take half its coefficient (-300). Square it (90000) and add it to both sides. Add '90000' to each side of the equation. -600x + 90000 + x2 = -70000 + 90000 Reorder the terms: 90000 + -600x + x2 = -70000 + 90000 Combine like terms: -70000 + 90000 = 20000 90000 + -600x + x2 = 20000 Factor a perfect square on the left side: (x + -300)(x + -300) = 20000 Calculate the square root of the right side: 141.421356237 Break this problem into two subproblems by setting (x + -300) equal to 141.421356237 and -141.421356237.Subproblem 1
x + -300 = 141.421356237 Simplifying x + -300 = 141.421356237 Reorder the terms: -300 + x = 141.421356237 Solving -300 + x = 141.421356237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '300' to each side of the equation. -300 + 300 + x = 141.421356237 + 300 Combine like terms: -300 + 300 = 0 0 + x = 141.421356237 + 300 x = 141.421356237 + 300 Combine like terms: 141.421356237 + 300 = 441.421356237 x = 441.421356237 Simplifying x = 441.421356237Subproblem 2
x + -300 = -141.421356237 Simplifying x + -300 = -141.421356237 Reorder the terms: -300 + x = -141.421356237 Solving -300 + x = -141.421356237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '300' to each side of the equation. -300 + 300 + x = -141.421356237 + 300 Combine like terms: -300 + 300 = 0 0 + x = -141.421356237 + 300 x = -141.421356237 + 300 Combine like terms: -141.421356237 + 300 = 158.578643763 x = 158.578643763 Simplifying x = 158.578643763Solution
The solution to the problem is based on the solutions from the subproblems. x = {441.421356237, 158.578643763}
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