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Simplifying (x + 50)(x) = 36 Reorder the terms: (50 + x)(x) = 36 Reorder the terms for easier multiplication: x(50 + x) = 36 (50 * x + x * x) = 36 (50x + x2) = 36 Solving 50x + x2 = 36 Solving for variable 'x'. Reorder the terms: -36 + 50x + x2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + 50x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 50x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 50x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 50x + x2 = 0 + 36 50x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 50x + x2 = 36 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 = 36 + 625 Reorder the terms: 625 + 50x + x2 = 36 + 625 Combine like terms: 36 + 625 = 661 625 + 50x + x2 = 661 Factor a perfect square on the left side: (x + 25)(x + 25) = 661 Calculate the square root of the right side: 25.709920264 Break this problem into two subproblems by setting (x + 25) equal to 25.709920264 and -25.709920264.Subproblem 1
x + 25 = 25.709920264 Simplifying x + 25 = 25.709920264 Reorder the terms: 25 + x = 25.709920264 Solving 25 + x = 25.709920264 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 = 25.709920264 + -25 Combine like terms: 25 + -25 = 0 0 + x = 25.709920264 + -25 x = 25.709920264 + -25 Combine like terms: 25.709920264 + -25 = 0.709920264 x = 0.709920264 Simplifying x = 0.709920264Subproblem 2
x + 25 = -25.709920264 Simplifying x + 25 = -25.709920264 Reorder the terms: 25 + x = -25.709920264 Solving 25 + x = -25.709920264 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 = -25.709920264 + -25 Combine like terms: 25 + -25 = 0 0 + x = -25.709920264 + -25 x = -25.709920264 + -25 Combine like terms: -25.709920264 + -25 = -50.709920264 x = -50.709920264 Simplifying x = -50.709920264Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.709920264, -50.709920264}
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