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Simplifying x2 + 100x + 100 = 408 Reorder the terms: 100 + 100x + x2 = 408 Solving 100 + 100x + x2 = 408 Solving for variable 'x'. Reorder the terms: 100 + -408 + 100x + x2 = 408 + -408 Combine like terms: 100 + -408 = -308 -308 + 100x + x2 = 408 + -408 Combine like terms: 408 + -408 = 0 -308 + 100x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '308' to each side of the equation. -308 + 100x + 308 + x2 = 0 + 308 Reorder the terms: -308 + 308 + 100x + x2 = 0 + 308 Combine like terms: -308 + 308 = 0 0 + 100x + x2 = 0 + 308 100x + x2 = 0 + 308 Combine like terms: 0 + 308 = 308 100x + x2 = 308 The x term is 100x. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100x + 2500 + x2 = 308 + 2500 Reorder the terms: 2500 + 100x + x2 = 308 + 2500 Combine like terms: 308 + 2500 = 2808 2500 + 100x + x2 = 2808 Factor a perfect square on the left side: (x + 50)(x + 50) = 2808 Calculate the square root of the right side: 52.990565198 Break this problem into two subproblems by setting (x + 50) equal to 52.990565198 and -52.990565198.Subproblem 1
x + 50 = 52.990565198 Simplifying x + 50 = 52.990565198 Reorder the terms: 50 + x = 52.990565198 Solving 50 + x = 52.990565198 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = 52.990565198 + -50 Combine like terms: 50 + -50 = 0 0 + x = 52.990565198 + -50 x = 52.990565198 + -50 Combine like terms: 52.990565198 + -50 = 2.990565198 x = 2.990565198 Simplifying x = 2.990565198Subproblem 2
x + 50 = -52.990565198 Simplifying x + 50 = -52.990565198 Reorder the terms: 50 + x = -52.990565198 Solving 50 + x = -52.990565198 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = -52.990565198 + -50 Combine like terms: 50 + -50 = 0 0 + x = -52.990565198 + -50 x = -52.990565198 + -50 Combine like terms: -52.990565198 + -50 = -102.990565198 x = -102.990565198 Simplifying x = -102.990565198Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.990565198, -102.990565198}
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