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Simplifying x(x + 50) = 150 Reorder the terms: x(50 + x) = 150 (50 * x + x * x) = 150 (50x + x2) = 150 Solving 50x + x2 = 150 Solving for variable 'x'. Reorder the terms: -150 + 50x + x2 = 150 + -150 Combine like terms: 150 + -150 = 0 -150 + 50x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '150' to each side of the equation. -150 + 50x + 150 + x2 = 0 + 150 Reorder the terms: -150 + 150 + 50x + x2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + 50x + x2 = 0 + 150 50x + x2 = 0 + 150 Combine like terms: 0 + 150 = 150 50x + x2 = 150 The x term is 50x. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50x + 625 + x2 = 150 + 625 Reorder the terms: 625 + 50x + x2 = 150 + 625 Combine like terms: 150 + 625 = 775 625 + 50x + x2 = 775 Factor a perfect square on the left side: (x + 25)(x + 25) = 775 Calculate the square root of the right side: 27.838821814 Break this problem into two subproblems by setting (x + 25) equal to 27.838821814 and -27.838821814.Subproblem 1
x + 25 = 27.838821814 Simplifying x + 25 = 27.838821814 Reorder the terms: 25 + x = 27.838821814 Solving 25 + x = 27.838821814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 27.838821814 + -25 Combine like terms: 25 + -25 = 0 0 + x = 27.838821814 + -25 x = 27.838821814 + -25 Combine like terms: 27.838821814 + -25 = 2.838821814 x = 2.838821814 Simplifying x = 2.838821814Subproblem 2
x + 25 = -27.838821814 Simplifying x + 25 = -27.838821814 Reorder the terms: 25 + x = -27.838821814 Solving 25 + x = -27.838821814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = -27.838821814 + -25 Combine like terms: 25 + -25 = 0 0 + x = -27.838821814 + -25 x = -27.838821814 + -25 Combine like terms: -27.838821814 + -25 = -52.838821814 x = -52.838821814 Simplifying x = -52.838821814Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.838821814, -52.838821814}
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