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Simplifying x(x + -7) = 1150 Reorder the terms: x(-7 + x) = 1150 (-7 * x + x * x) = 1150 (-7x + x2) = 1150 Solving -7x + x2 = 1150 Solving for variable 'x'. Reorder the terms: -1150 + -7x + x2 = 1150 + -1150 Combine like terms: 1150 + -1150 = 0 -1150 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1150' to each side of the equation. -1150 + -7x + 1150 + x2 = 0 + 1150 Reorder the terms: -1150 + 1150 + -7x + x2 = 0 + 1150 Combine like terms: -1150 + 1150 = 0 0 + -7x + x2 = 0 + 1150 -7x + x2 = 0 + 1150 Combine like terms: 0 + 1150 = 1150 -7x + x2 = 1150 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 1150 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 1150 + 12.25 Combine like terms: 1150 + 12.25 = 1162.25 12.25 + -7x + x2 = 1162.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 1162.25 Calculate the square root of the right side: 34.091787867 Break this problem into two subproblems by setting (x + -3.5) equal to 34.091787867 and -34.091787867.Subproblem 1
x + -3.5 = 34.091787867 Simplifying x + -3.5 = 34.091787867 Reorder the terms: -3.5 + x = 34.091787867 Solving -3.5 + x = 34.091787867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 34.091787867 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 34.091787867 + 3.5 x = 34.091787867 + 3.5 Combine like terms: 34.091787867 + 3.5 = 37.591787867 x = 37.591787867 Simplifying x = 37.591787867Subproblem 2
x + -3.5 = -34.091787867 Simplifying x + -3.5 = -34.091787867 Reorder the terms: -3.5 + x = -34.091787867 Solving -3.5 + x = -34.091787867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -34.091787867 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -34.091787867 + 3.5 x = -34.091787867 + 3.5 Combine like terms: -34.091787867 + 3.5 = -30.591787867 x = -30.591787867 Simplifying x = -30.591787867Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.591787867, -30.591787867}
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