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Simplifying 1220 = x(150 + x) 1220 = (150 * x + x * x) 1220 = (150x + x2) Solving 1220 = 150x + x2 Solving for variable 'x'. Reorder the terms: 1220 + -150x + -1x2 = 150x + -150x + x2 + -1x2 Combine like terms: 150x + -150x = 0 1220 + -150x + -1x2 = 0 + x2 + -1x2 1220 + -150x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1220 + -150x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1220 + 150x + x2 = 0 Move the constant term to the right: Add '1220' to each side of the equation. -1220 + 150x + 1220 + x2 = 0 + 1220 Reorder the terms: -1220 + 1220 + 150x + x2 = 0 + 1220 Combine like terms: -1220 + 1220 = 0 0 + 150x + x2 = 0 + 1220 150x + x2 = 0 + 1220 Combine like terms: 0 + 1220 = 1220 150x + x2 = 1220 The x term is 150x. Take half its coefficient (75). Square it (5625) and add it to both sides. Add '5625' to each side of the equation. 150x + 5625 + x2 = 1220 + 5625 Reorder the terms: 5625 + 150x + x2 = 1220 + 5625 Combine like terms: 1220 + 5625 = 6845 5625 + 150x + x2 = 6845 Factor a perfect square on the left side: (x + 75)(x + 75) = 6845 Calculate the square root of the right side: 82.734515167 Break this problem into two subproblems by setting (x + 75) equal to 82.734515167 and -82.734515167.Subproblem 1
x + 75 = 82.734515167 Simplifying x + 75 = 82.734515167 Reorder the terms: 75 + x = 82.734515167 Solving 75 + x = 82.734515167 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + x = 82.734515167 + -75 Combine like terms: 75 + -75 = 0 0 + x = 82.734515167 + -75 x = 82.734515167 + -75 Combine like terms: 82.734515167 + -75 = 7.734515167 x = 7.734515167 Simplifying x = 7.734515167Subproblem 2
x + 75 = -82.734515167 Simplifying x + 75 = -82.734515167 Reorder the terms: 75 + x = -82.734515167 Solving 75 + x = -82.734515167 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + x = -82.734515167 + -75 Combine like terms: 75 + -75 = 0 0 + x = -82.734515167 + -75 x = -82.734515167 + -75 Combine like terms: -82.734515167 + -75 = -157.734515167 x = -157.734515167 Simplifying x = -157.734515167Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.734515167, -157.734515167}
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