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Simplifying x2 + 70x + -180 = 0 Reorder the terms: -180 + 70x + x2 = 0 Solving -180 + 70x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + 70x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + 70x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 70x + x2 = 0 + 180 70x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 70x + x2 = 180 The x term is 70x. Take half its coefficient (35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. 70x + 1225 + x2 = 180 + 1225 Reorder the terms: 1225 + 70x + x2 = 180 + 1225 Combine like terms: 180 + 1225 = 1405 1225 + 70x + x2 = 1405 Factor a perfect square on the left side: (x + 35)(x + 35) = 1405 Calculate the square root of the right side: 37.483329628 Break this problem into two subproblems by setting (x + 35) equal to 37.483329628 and -37.483329628.Subproblem 1
x + 35 = 37.483329628 Simplifying x + 35 = 37.483329628 Reorder the terms: 35 + x = 37.483329628 Solving 35 + x = 37.483329628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + x = 37.483329628 + -35 Combine like terms: 35 + -35 = 0 0 + x = 37.483329628 + -35 x = 37.483329628 + -35 Combine like terms: 37.483329628 + -35 = 2.483329628 x = 2.483329628 Simplifying x = 2.483329628Subproblem 2
x + 35 = -37.483329628 Simplifying x + 35 = -37.483329628 Reorder the terms: 35 + x = -37.483329628 Solving 35 + x = -37.483329628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + x = -37.483329628 + -35 Combine like terms: 35 + -35 = 0 0 + x = -37.483329628 + -35 x = -37.483329628 + -35 Combine like terms: -37.483329628 + -35 = -72.483329628 x = -72.483329628 Simplifying x = -72.483329628Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.483329628, -72.483329628}
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