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Simplifying x2 + 50x = 15 Reorder the terms: 50x + x2 = 15 Solving 50x + x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + 50x + x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 50x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 50x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 50x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 50x + x2 = 0 + 15 50x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 50x + x2 = 15 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 = 15 + 625 Reorder the terms: 625 + 50x + x2 = 15 + 625 Combine like terms: 15 + 625 = 640 625 + 50x + x2 = 640 Factor a perfect square on the left side: (x + 25)(x + 25) = 640 Calculate the square root of the right side: 25.298221281 Break this problem into two subproblems by setting (x + 25) equal to 25.298221281 and -25.298221281.Subproblem 1
x + 25 = 25.298221281 Simplifying x + 25 = 25.298221281 Reorder the terms: 25 + x = 25.298221281 Solving 25 + x = 25.298221281 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 = 25.298221281 + -25 Combine like terms: 25 + -25 = 0 0 + x = 25.298221281 + -25 x = 25.298221281 + -25 Combine like terms: 25.298221281 + -25 = 0.298221281 x = 0.298221281 Simplifying x = 0.298221281Subproblem 2
x + 25 = -25.298221281 Simplifying x + 25 = -25.298221281 Reorder the terms: 25 + x = -25.298221281 Solving 25 + x = -25.298221281 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 = -25.298221281 + -25 Combine like terms: 25 + -25 = 0 0 + x = -25.298221281 + -25 x = -25.298221281 + -25 Combine like terms: -25.298221281 + -25 = -50.298221281 x = -50.298221281 Simplifying x = -50.298221281Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.298221281, -50.298221281}
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