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Simplifying 0.001x(x + -5) = 700 Reorder the terms: 0.001x(-5 + x) = 700 (-5 * 0.001x + x * 0.001x) = 700 (-0.005x + 0.001x2) = 700 Solving -0.005x + 0.001x2 = 700 Solving for variable 'x'. Reorder the terms: -700 + -0.005x + 0.001x2 = 700 + -700 Combine like terms: 700 + -700 = 0 -700 + -0.005x + 0.001x2 = 0 Begin completing the square. Divide all terms by 0.001 the coefficient of the squared term: Divide each side by '0.001'. -700000 + -5x + x2 = 0 Move the constant term to the right: Add '700000' to each side of the equation. -700000 + -5x + 700000 + x2 = 0 + 700000 Reorder the terms: -700000 + 700000 + -5x + x2 = 0 + 700000 Combine like terms: -700000 + 700000 = 0 0 + -5x + x2 = 0 + 700000 -5x + x2 = 0 + 700000 Combine like terms: 0 + 700000 = 700000 -5x + x2 = 700000 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 700000 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 700000 + 6.25 Combine like terms: 700000 + 6.25 = 700006.25 6.25 + -5x + x2 = 700006.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 700006.25 Calculate the square root of the right side: 836.663761615 Break this problem into two subproblems by setting (x + -2.5) equal to 836.663761615 and -836.663761615.Subproblem 1
x + -2.5 = 836.663761615 Simplifying x + -2.5 = 836.663761615 Reorder the terms: -2.5 + x = 836.663761615 Solving -2.5 + x = 836.663761615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 836.663761615 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 836.663761615 + 2.5 x = 836.663761615 + 2.5 Combine like terms: 836.663761615 + 2.5 = 839.163761615 x = 839.163761615 Simplifying x = 839.163761615Subproblem 2
x + -2.5 = -836.663761615 Simplifying x + -2.5 = -836.663761615 Reorder the terms: -2.5 + x = -836.663761615 Solving -2.5 + x = -836.663761615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -836.663761615 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -836.663761615 + 2.5 x = -836.663761615 + 2.5 Combine like terms: -836.663761615 + 2.5 = -834.163761615 x = -834.163761615 Simplifying x = -834.163761615Solution
The solution to the problem is based on the solutions from the subproblems. x = {839.163761615, -834.163761615}
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