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Simplifying -0.01x2 + 8x + -700 = 0 Reorder the terms: -700 + 8x + -0.01x2 = 0 Solving -700 + 8x + -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 + -800x + x2 = 0 Move the constant term to the right: Add '-70000' to each side of the equation. 70000 + -800x + -70000 + x2 = 0 + -70000 Reorder the terms: 70000 + -70000 + -800x + x2 = 0 + -70000 Combine like terms: 70000 + -70000 = 0 0 + -800x + x2 = 0 + -70000 -800x + x2 = 0 + -70000 Combine like terms: 0 + -70000 = -70000 -800x + x2 = -70000 The x term is -800x. Take half its coefficient (-400). Square it (160000) and add it to both sides. Add '160000' to each side of the equation. -800x + 160000 + x2 = -70000 + 160000 Reorder the terms: 160000 + -800x + x2 = -70000 + 160000 Combine like terms: -70000 + 160000 = 90000 160000 + -800x + x2 = 90000 Factor a perfect square on the left side: (x + -400)(x + -400) = 90000 Calculate the square root of the right side: 300 Break this problem into two subproblems by setting (x + -400) equal to 300 and -300.Subproblem 1
x + -400 = 300 Simplifying x + -400 = 300 Reorder the terms: -400 + x = 300 Solving -400 + x = 300 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '400' to each side of the equation. -400 + 400 + x = 300 + 400 Combine like terms: -400 + 400 = 0 0 + x = 300 + 400 x = 300 + 400 Combine like terms: 300 + 400 = 700 x = 700 Simplifying x = 700Subproblem 2
x + -400 = -300 Simplifying x + -400 = -300 Reorder the terms: -400 + x = -300 Solving -400 + x = -300 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '400' to each side of the equation. -400 + 400 + x = -300 + 400 Combine like terms: -400 + 400 = 0 0 + x = -300 + 400 x = -300 + 400 Combine like terms: -300 + 400 = 100 x = 100 Simplifying x = 100Solution
The solution to the problem is based on the solutions from the subproblems. x = {700, 100}
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