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Simplifying 2x2 + 23x = 154 Reorder the terms: 23x + 2x2 = 154 Solving 23x + 2x2 = 154 Solving for variable 'x'. Reorder the terms: -154 + 23x + 2x2 = 154 + -154 Combine like terms: 154 + -154 = 0 -154 + 23x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -77 + 11.5x + x2 = 0 Move the constant term to the right: Add '77' to each side of the equation. -77 + 11.5x + 77 + x2 = 0 + 77 Reorder the terms: -77 + 77 + 11.5x + x2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + 11.5x + x2 = 0 + 77 11.5x + x2 = 0 + 77 Combine like terms: 0 + 77 = 77 11.5x + x2 = 77 The x term is 11.5x. Take half its coefficient (5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. 11.5x + 33.0625 + x2 = 77 + 33.0625 Reorder the terms: 33.0625 + 11.5x + x2 = 77 + 33.0625 Combine like terms: 77 + 33.0625 = 110.0625 33.0625 + 11.5x + x2 = 110.0625 Factor a perfect square on the left side: (x + 5.75)(x + 5.75) = 110.0625 Calculate the square root of the right side: 10.491067629 Break this problem into two subproblems by setting (x + 5.75) equal to 10.491067629 and -10.491067629.Subproblem 1
x + 5.75 = 10.491067629 Simplifying x + 5.75 = 10.491067629 Reorder the terms: 5.75 + x = 10.491067629 Solving 5.75 + x = 10.491067629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + x = 10.491067629 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = 10.491067629 + -5.75 x = 10.491067629 + -5.75 Combine like terms: 10.491067629 + -5.75 = 4.741067629 x = 4.741067629 Simplifying x = 4.741067629Subproblem 2
x + 5.75 = -10.491067629 Simplifying x + 5.75 = -10.491067629 Reorder the terms: 5.75 + x = -10.491067629 Solving 5.75 + x = -10.491067629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + x = -10.491067629 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = -10.491067629 + -5.75 x = -10.491067629 + -5.75 Combine like terms: -10.491067629 + -5.75 = -16.241067629 x = -16.241067629 Simplifying x = -16.241067629Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.741067629, -16.241067629}
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