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Simplifying x(670 + -1x) = 0.35 (670 * x + -1x * x) = 0.35 (670x + -1x2) = 0.35 Solving 670x + -1x2 = 0.35 Solving for variable 'x'. Reorder the terms: -0.35 + 670x + -1x2 = 0.35 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 -0.35 + 670x + -1x2 = 0.00 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.35 + -670x + x2 = 0.00 Move the constant term to the right: Add '-0.35' to each side of the equation. 0.35 + -670x + -0.35 + x2 = 0.00 + -0.35 Reorder the terms: 0.35 + -0.35 + -670x + x2 = 0.00 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + -670x + x2 = 0.00 + -0.35 -670x + x2 = 0.00 + -0.35 Combine like terms: 0.00 + -0.35 = -0.35 -670x + x2 = -0.35 The x term is -670x. Take half its coefficient (-335). Square it (112225) and add it to both sides. Add '112225' to each side of the equation. -670x + 112225 + x2 = -0.35 + 112225 Reorder the terms: 112225 + -670x + x2 = -0.35 + 112225 Combine like terms: -0.35 + 112225 = 112224.65 112225 + -670x + x2 = 112224.65 Factor a perfect square on the left side: (x + -335)(x + -335) = 112224.65 Calculate the square root of the right side: 334.999477612 Break this problem into two subproblems by setting (x + -335) equal to 334.999477612 and -334.999477612.Subproblem 1
x + -335 = 334.999477612 Simplifying x + -335 = 334.999477612 Reorder the terms: -335 + x = 334.999477612 Solving -335 + x = 334.999477612 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '335' to each side of the equation. -335 + 335 + x = 334.999477612 + 335 Combine like terms: -335 + 335 = 0 0 + x = 334.999477612 + 335 x = 334.999477612 + 335 Combine like terms: 334.999477612 + 335 = 669.999477612 x = 669.999477612 Simplifying x = 669.999477612Subproblem 2
x + -335 = -334.999477612 Simplifying x + -335 = -334.999477612 Reorder the terms: -335 + x = -334.999477612 Solving -335 + x = -334.999477612 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '335' to each side of the equation. -335 + 335 + x = -334.999477612 + 335 Combine like terms: -335 + 335 = 0 0 + x = -334.999477612 + 335 x = -334.999477612 + 335 Combine like terms: -334.999477612 + 335 = 0.000522388 x = 0.000522388 Simplifying x = 0.000522388Solution
The solution to the problem is based on the solutions from the subproblems. x = {669.999477612, 0.000522388}
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