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Simplifying 234 = x(x + 20) Reorder the terms: 234 = x(20 + x) 234 = (20 * x + x * x) 234 = (20x + x2) Solving 234 = 20x + x2 Solving for variable 'x'. Reorder the terms: 234 + -20x + -1x2 = 20x + -20x + x2 + -1x2 Combine like terms: 20x + -20x = 0 234 + -20x + -1x2 = 0 + x2 + -1x2 234 + -20x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 234 + -20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -234 + 20x + x2 = 0 Move the constant term to the right: Add '234' to each side of the equation. -234 + 20x + 234 + x2 = 0 + 234 Reorder the terms: -234 + 234 + 20x + x2 = 0 + 234 Combine like terms: -234 + 234 = 0 0 + 20x + x2 = 0 + 234 20x + x2 = 0 + 234 Combine like terms: 0 + 234 = 234 20x + x2 = 234 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 234 + 100 Reorder the terms: 100 + 20x + x2 = 234 + 100 Combine like terms: 234 + 100 = 334 100 + 20x + x2 = 334 Factor a perfect square on the left side: (x + 10)(x + 10) = 334 Calculate the square root of the right side: 18.275666882 Break this problem into two subproblems by setting (x + 10) equal to 18.275666882 and -18.275666882.Subproblem 1
x + 10 = 18.275666882 Simplifying x + 10 = 18.275666882 Reorder the terms: 10 + x = 18.275666882 Solving 10 + x = 18.275666882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 18.275666882 + -10 Combine like terms: 10 + -10 = 0 0 + x = 18.275666882 + -10 x = 18.275666882 + -10 Combine like terms: 18.275666882 + -10 = 8.275666882 x = 8.275666882 Simplifying x = 8.275666882Subproblem 2
x + 10 = -18.275666882 Simplifying x + 10 = -18.275666882 Reorder the terms: 10 + x = -18.275666882 Solving 10 + x = -18.275666882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -18.275666882 + -10 Combine like terms: 10 + -10 = 0 0 + x = -18.275666882 + -10 x = -18.275666882 + -10 Combine like terms: -18.275666882 + -10 = -28.275666882 x = -28.275666882 Simplifying x = -28.275666882Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.275666882, -28.275666882}
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