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Simplifying x2 + 10x + -208 = 0 Reorder the terms: -208 + 10x + x2 = 0 Solving -208 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '208' to each side of the equation. -208 + 10x + 208 + x2 = 0 + 208 Reorder the terms: -208 + 208 + 10x + x2 = 0 + 208 Combine like terms: -208 + 208 = 0 0 + 10x + x2 = 0 + 208 10x + x2 = 0 + 208 Combine like terms: 0 + 208 = 208 10x + x2 = 208 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 208 + 25 Reorder the terms: 25 + 10x + x2 = 208 + 25 Combine like terms: 208 + 25 = 233 25 + 10x + x2 = 233 Factor a perfect square on the left side: (x + 5)(x + 5) = 233 Calculate the square root of the right side: 15.264337522 Break this problem into two subproblems by setting (x + 5) equal to 15.264337522 and -15.264337522.Subproblem 1
x + 5 = 15.264337522 Simplifying x + 5 = 15.264337522 Reorder the terms: 5 + x = 15.264337522 Solving 5 + x = 15.264337522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 15.264337522 + -5 Combine like terms: 5 + -5 = 0 0 + x = 15.264337522 + -5 x = 15.264337522 + -5 Combine like terms: 15.264337522 + -5 = 10.264337522 x = 10.264337522 Simplifying x = 10.264337522Subproblem 2
x + 5 = -15.264337522 Simplifying x + 5 = -15.264337522 Reorder the terms: 5 + x = -15.264337522 Solving 5 + x = -15.264337522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -15.264337522 + -5 Combine like terms: 5 + -5 = 0 0 + x = -15.264337522 + -5 x = -15.264337522 + -5 Combine like terms: -15.264337522 + -5 = -20.264337522 x = -20.264337522 Simplifying x = -20.264337522Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.264337522, -20.264337522}
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