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Simplifying x2 + -150x + 2250 = 0 Reorder the terms: 2250 + -150x + x2 = 0 Solving 2250 + -150x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2250' to each side of the equation. 2250 + -150x + -2250 + x2 = 0 + -2250 Reorder the terms: 2250 + -2250 + -150x + x2 = 0 + -2250 Combine like terms: 2250 + -2250 = 0 0 + -150x + x2 = 0 + -2250 -150x + x2 = 0 + -2250 Combine like terms: 0 + -2250 = -2250 -150x + x2 = -2250 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 = -2250 + 5625 Reorder the terms: 5625 + -150x + x2 = -2250 + 5625 Combine like terms: -2250 + 5625 = 3375 5625 + -150x + x2 = 3375 Factor a perfect square on the left side: (x + -75)(x + -75) = 3375 Calculate the square root of the right side: 58.094750193 Break this problem into two subproblems by setting (x + -75) equal to 58.094750193 and -58.094750193.Subproblem 1
x + -75 = 58.094750193 Simplifying x + -75 = 58.094750193 Reorder the terms: -75 + x = 58.094750193 Solving -75 + x = 58.094750193 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 = 58.094750193 + 75 Combine like terms: -75 + 75 = 0 0 + x = 58.094750193 + 75 x = 58.094750193 + 75 Combine like terms: 58.094750193 + 75 = 133.094750193 x = 133.094750193 Simplifying x = 133.094750193Subproblem 2
x + -75 = -58.094750193 Simplifying x + -75 = -58.094750193 Reorder the terms: -75 + x = -58.094750193 Solving -75 + x = -58.094750193 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 = -58.094750193 + 75 Combine like terms: -75 + 75 = 0 0 + x = -58.094750193 + 75 x = -58.094750193 + 75 Combine like terms: -58.094750193 + 75 = 16.905249807 x = 16.905249807 Simplifying x = 16.905249807Solution
The solution to the problem is based on the solutions from the subproblems. x = {133.094750193, 16.905249807}
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