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Simplifying x2 + -50x + 15 = 0 Reorder the terms: 15 + -50x + x2 = 0 Solving 15 + -50x + x2 = 0 Solving for variable 'x'. 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 = 610 625 + -50x + x2 = 610 Factor a perfect square on the left side: (x + -25)(x + -25) = 610 Calculate the square root of the right side: 24.69817807 Break this problem into two subproblems by setting (x + -25) equal to 24.69817807 and -24.69817807.Subproblem 1
x + -25 = 24.69817807 Simplifying x + -25 = 24.69817807 Reorder the terms: -25 + x = 24.69817807 Solving -25 + x = 24.69817807 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 = 24.69817807 + 25 Combine like terms: -25 + 25 = 0 0 + x = 24.69817807 + 25 x = 24.69817807 + 25 Combine like terms: 24.69817807 + 25 = 49.69817807 x = 49.69817807 Simplifying x = 49.69817807Subproblem 2
x + -25 = -24.69817807 Simplifying x + -25 = -24.69817807 Reorder the terms: -25 + x = -24.69817807 Solving -25 + x = -24.69817807 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 = -24.69817807 + 25 Combine like terms: -25 + 25 = 0 0 + x = -24.69817807 + 25 x = -24.69817807 + 25 Combine like terms: -24.69817807 + 25 = 0.30182193 x = 0.30182193 Simplifying x = 0.30182193Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.69817807, 0.30182193}
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