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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 = 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 = -0.30182193 x = -0.30182193 Simplifying x = -0.30182193Subproblem 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 = -49.69817807 x = -49.69817807 Simplifying x = -49.69817807Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.30182193, -49.69817807}
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