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Simplifying x(x + 2) = 100 Reorder the terms: x(2 + x) = 100 (2 * x + x * x) = 100 (2x + x2) = 100 Solving 2x + x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + 2x + x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 2x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 2x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 2x + x2 = 0 + 100 2x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 2x + x2 = 100 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 100 + 1 Reorder the terms: 1 + 2x + x2 = 100 + 1 Combine like terms: 100 + 1 = 101 1 + 2x + x2 = 101 Factor a perfect square on the left side: (x + 1)(x + 1) = 101 Calculate the square root of the right side: 10.049875621 Break this problem into two subproblems by setting (x + 1) equal to 10.049875621 and -10.049875621.Subproblem 1
x + 1 = 10.049875621 Simplifying x + 1 = 10.049875621 Reorder the terms: 1 + x = 10.049875621 Solving 1 + x = 10.049875621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 10.049875621 + -1 Combine like terms: 1 + -1 = 0 0 + x = 10.049875621 + -1 x = 10.049875621 + -1 Combine like terms: 10.049875621 + -1 = 9.049875621 x = 9.049875621 Simplifying x = 9.049875621Subproblem 2
x + 1 = -10.049875621 Simplifying x + 1 = -10.049875621 Reorder the terms: 1 + x = -10.049875621 Solving 1 + x = -10.049875621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -10.049875621 + -1 Combine like terms: 1 + -1 = 0 0 + x = -10.049875621 + -1 x = -10.049875621 + -1 Combine like terms: -10.049875621 + -1 = -11.049875621 x = -11.049875621 Simplifying x = -11.049875621Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.049875621, -11.049875621}
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