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Simplifying x2 + 100x + -14900 = 0 Reorder the terms: -14900 + 100x + x2 = 0 Solving -14900 + 100x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '14900' to each side of the equation. -14900 + 100x + 14900 + x2 = 0 + 14900 Reorder the terms: -14900 + 14900 + 100x + x2 = 0 + 14900 Combine like terms: -14900 + 14900 = 0 0 + 100x + x2 = 0 + 14900 100x + x2 = 0 + 14900 Combine like terms: 0 + 14900 = 14900 100x + x2 = 14900 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 = 14900 + 2500 Reorder the terms: 2500 + 100x + x2 = 14900 + 2500 Combine like terms: 14900 + 2500 = 17400 2500 + 100x + x2 = 17400 Factor a perfect square on the left side: (x + 50)(x + 50) = 17400 Calculate the square root of the right side: 131.909059583 Break this problem into two subproblems by setting (x + 50) equal to 131.909059583 and -131.909059583.Subproblem 1
x + 50 = 131.909059583 Simplifying x + 50 = 131.909059583 Reorder the terms: 50 + x = 131.909059583 Solving 50 + x = 131.909059583 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 = 131.909059583 + -50 Combine like terms: 50 + -50 = 0 0 + x = 131.909059583 + -50 x = 131.909059583 + -50 Combine like terms: 131.909059583 + -50 = 81.909059583 x = 81.909059583 Simplifying x = 81.909059583Subproblem 2
x + 50 = -131.909059583 Simplifying x + 50 = -131.909059583 Reorder the terms: 50 + x = -131.909059583 Solving 50 + x = -131.909059583 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 = -131.909059583 + -50 Combine like terms: 50 + -50 = 0 0 + x = -131.909059583 + -50 x = -131.909059583 + -50 Combine like terms: -131.909059583 + -50 = -181.909059583 x = -181.909059583 Simplifying x = -181.909059583Solution
The solution to the problem is based on the solutions from the subproblems. x = {81.909059583, -181.909059583}
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