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Simplifying x2 + 175x = 1600 * 7 Reorder the terms: 175x + x2 = 1600 * 7 Multiply 1600 * 7 175x + x2 = 11200 Solving 175x + x2 = 11200 Solving for variable 'x'. Reorder the terms: -11200 + 175x + x2 = 11200 + -11200 Combine like terms: 11200 + -11200 = 0 -11200 + 175x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11200' to each side of the equation. -11200 + 175x + 11200 + x2 = 0 + 11200 Reorder the terms: -11200 + 11200 + 175x + x2 = 0 + 11200 Combine like terms: -11200 + 11200 = 0 0 + 175x + x2 = 0 + 11200 175x + x2 = 0 + 11200 Combine like terms: 0 + 11200 = 11200 175x + x2 = 11200 The x term is 175x. Take half its coefficient (87.5). Square it (7656.25) and add it to both sides. Add '7656.25' to each side of the equation. 175x + 7656.25 + x2 = 11200 + 7656.25 Reorder the terms: 7656.25 + 175x + x2 = 11200 + 7656.25 Combine like terms: 11200 + 7656.25 = 18856.25 7656.25 + 175x + x2 = 18856.25 Factor a perfect square on the left side: (x + 87.5)(x + 87.5) = 18856.25 Calculate the square root of the right side: 137.318061449 Break this problem into two subproblems by setting (x + 87.5) equal to 137.318061449 and -137.318061449.Subproblem 1
x + 87.5 = 137.318061449 Simplifying x + 87.5 = 137.318061449 Reorder the terms: 87.5 + x = 137.318061449 Solving 87.5 + x = 137.318061449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-87.5' to each side of the equation. 87.5 + -87.5 + x = 137.318061449 + -87.5 Combine like terms: 87.5 + -87.5 = 0.0 0.0 + x = 137.318061449 + -87.5 x = 137.318061449 + -87.5 Combine like terms: 137.318061449 + -87.5 = 49.818061449 x = 49.818061449 Simplifying x = 49.818061449Subproblem 2
x + 87.5 = -137.318061449 Simplifying x + 87.5 = -137.318061449 Reorder the terms: 87.5 + x = -137.318061449 Solving 87.5 + x = -137.318061449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-87.5' to each side of the equation. 87.5 + -87.5 + x = -137.318061449 + -87.5 Combine like terms: 87.5 + -87.5 = 0.0 0.0 + x = -137.318061449 + -87.5 x = -137.318061449 + -87.5 Combine like terms: -137.318061449 + -87.5 = -224.818061449 x = -224.818061449 Simplifying x = -224.818061449Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.818061449, -224.818061449}
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