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Simplifying 276 = x(x + -20) Reorder the terms: 276 = x(-20 + x) 276 = (-20 * x + x * x) 276 = (-20x + x2) Solving 276 = -20x + x2 Solving for variable 'x'. Reorder the terms: 276 + 20x + -1x2 = -20x + 20x + x2 + -1x2 Combine like terms: -20x + 20x = 0 276 + 20x + -1x2 = 0 + x2 + -1x2 276 + 20x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 276 + 20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -276 + -20x + x2 = 0 Move the constant term to the right: Add '276' to each side of the equation. -276 + -20x + 276 + x2 = 0 + 276 Reorder the terms: -276 + 276 + -20x + x2 = 0 + 276 Combine like terms: -276 + 276 = 0 0 + -20x + x2 = 0 + 276 -20x + x2 = 0 + 276 Combine like terms: 0 + 276 = 276 -20x + x2 = 276 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 = 276 + 100 Reorder the terms: 100 + -20x + x2 = 276 + 100 Combine like terms: 276 + 100 = 376 100 + -20x + x2 = 376 Factor a perfect square on the left side: (x + -10)(x + -10) = 376 Calculate the square root of the right side: 19.39071943 Break this problem into two subproblems by setting (x + -10) equal to 19.39071943 and -19.39071943.Subproblem 1
x + -10 = 19.39071943 Simplifying x + -10 = 19.39071943 Reorder the terms: -10 + x = 19.39071943 Solving -10 + x = 19.39071943 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 = 19.39071943 + 10 Combine like terms: -10 + 10 = 0 0 + x = 19.39071943 + 10 x = 19.39071943 + 10 Combine like terms: 19.39071943 + 10 = 29.39071943 x = 29.39071943 Simplifying x = 29.39071943Subproblem 2
x + -10 = -19.39071943 Simplifying x + -10 = -19.39071943 Reorder the terms: -10 + x = -19.39071943 Solving -10 + x = -19.39071943 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 = -19.39071943 + 10 Combine like terms: -10 + 10 = 0 0 + x = -19.39071943 + 10 x = -19.39071943 + 10 Combine like terms: -19.39071943 + 10 = -9.39071943 x = -9.39071943 Simplifying x = -9.39071943Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.39071943, -9.39071943}
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