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Simplifying X2 + -150X + 2125 = 0 Reorder the terms: 2125 + -150X + X2 = 0 Solving 2125 + -150X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '-2125' to each side of the equation. 2125 + -150X + -2125 + X2 = 0 + -2125 Reorder the terms: 2125 + -2125 + -150X + X2 = 0 + -2125 Combine like terms: 2125 + -2125 = 0 0 + -150X + X2 = 0 + -2125 -150X + X2 = 0 + -2125 Combine like terms: 0 + -2125 = -2125 -150X + X2 = -2125 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 = -2125 + 5625 Reorder the terms: 5625 + -150X + X2 = -2125 + 5625 Combine like terms: -2125 + 5625 = 3500 5625 + -150X + X2 = 3500 Factor a perfect square on the left side: (X + -75)(X + -75) = 3500 Calculate the square root of the right side: 59.160797831 Break this problem into two subproblems by setting (X + -75) equal to 59.160797831 and -59.160797831.Subproblem 1
X + -75 = 59.160797831 Simplifying X + -75 = 59.160797831 Reorder the terms: -75 + X = 59.160797831 Solving -75 + X = 59.160797831 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 = 59.160797831 + 75 Combine like terms: -75 + 75 = 0 0 + X = 59.160797831 + 75 X = 59.160797831 + 75 Combine like terms: 59.160797831 + 75 = 134.160797831 X = 134.160797831 Simplifying X = 134.160797831Subproblem 2
X + -75 = -59.160797831 Simplifying X + -75 = -59.160797831 Reorder the terms: -75 + X = -59.160797831 Solving -75 + X = -59.160797831 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 = -59.160797831 + 75 Combine like terms: -75 + 75 = 0 0 + X = -59.160797831 + 75 X = -59.160797831 + 75 Combine like terms: -59.160797831 + 75 = 15.839202169 X = 15.839202169 Simplifying X = 15.839202169Solution
The solution to the problem is based on the solutions from the subproblems. X = {134.160797831, 15.839202169}
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