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Simplifying x(x + -50) + -36 = 0 Reorder the terms: x(-50 + x) + -36 = 0 (-50 * x + x * x) + -36 = 0 (-50x + x2) + -36 = 0 Reorder the terms: -36 + -50x + x2 = 0 Solving -36 + -50x + x2 = 0 Solving for variable 'x'. 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 = 50.709920264 x = 50.709920264 Simplifying x = 50.709920264Subproblem 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 = -0.709920264 x = -0.709920264 Simplifying x = -0.709920264Solution
The solution to the problem is based on the solutions from the subproblems. x = {50.709920264, -0.709920264}
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