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Simplifying x2 + 50x + 47 = 0 Reorder the terms: 47 + 50x + x2 = 0 Solving 47 + 50x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-47' to each side of the equation. 47 + 50x + -47 + x2 = 0 + -47 Reorder the terms: 47 + -47 + 50x + x2 = 0 + -47 Combine like terms: 47 + -47 = 0 0 + 50x + x2 = 0 + -47 50x + x2 = 0 + -47 Combine like terms: 0 + -47 = -47 50x + x2 = -47 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 = -47 + 625 Reorder the terms: 625 + 50x + x2 = -47 + 625 Combine like terms: -47 + 625 = 578 625 + 50x + x2 = 578 Factor a perfect square on the left side: (x + 25)(x + 25) = 578 Calculate the square root of the right side: 24.04163056 Break this problem into two subproblems by setting (x + 25) equal to 24.04163056 and -24.04163056.Subproblem 1
x + 25 = 24.04163056 Simplifying x + 25 = 24.04163056 Reorder the terms: 25 + x = 24.04163056 Solving 25 + x = 24.04163056 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 = 24.04163056 + -25 Combine like terms: 25 + -25 = 0 0 + x = 24.04163056 + -25 x = 24.04163056 + -25 Combine like terms: 24.04163056 + -25 = -0.95836944 x = -0.95836944 Simplifying x = -0.95836944Subproblem 2
x + 25 = -24.04163056 Simplifying x + 25 = -24.04163056 Reorder the terms: 25 + x = -24.04163056 Solving 25 + x = -24.04163056 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 = -24.04163056 + -25 Combine like terms: 25 + -25 = 0 0 + x = -24.04163056 + -25 x = -24.04163056 + -25 Combine like terms: -24.04163056 + -25 = -49.04163056 x = -49.04163056 Simplifying x = -49.04163056Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.95836944, -49.04163056}
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