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Simplifying x2 + 100x + -9 = 0 Reorder the terms: -9 + 100x + x2 = 0 Solving -9 + 100x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 100x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 100x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 100x + x2 = 0 + 9 100x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 100x + x2 = 9 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 = 9 + 2500 Reorder the terms: 2500 + 100x + x2 = 9 + 2500 Combine like terms: 9 + 2500 = 2509 2500 + 100x + x2 = 2509 Factor a perfect square on the left side: (x + 50)(x + 50) = 2509 Calculate the square root of the right side: 50.089919145 Break this problem into two subproblems by setting (x + 50) equal to 50.089919145 and -50.089919145.Subproblem 1
x + 50 = 50.089919145 Simplifying x + 50 = 50.089919145 Reorder the terms: 50 + x = 50.089919145 Solving 50 + x = 50.089919145 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 = 50.089919145 + -50 Combine like terms: 50 + -50 = 0 0 + x = 50.089919145 + -50 x = 50.089919145 + -50 Combine like terms: 50.089919145 + -50 = 0.089919145 x = 0.089919145 Simplifying x = 0.089919145Subproblem 2
x + 50 = -50.089919145 Simplifying x + 50 = -50.089919145 Reorder the terms: 50 + x = -50.089919145 Solving 50 + x = -50.089919145 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 = -50.089919145 + -50 Combine like terms: 50 + -50 = 0 0 + x = -50.089919145 + -50 x = -50.089919145 + -50 Combine like terms: -50.089919145 + -50 = -100.089919145 x = -100.089919145 Simplifying x = -100.089919145Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.089919145, -100.089919145}
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