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Simplifying -0.44x2 + 2.61x + 10 = 0 Reorder the terms: 10 + 2.61x + -0.44x2 = 0 Solving 10 + 2.61x + -0.44x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.44 the coefficient of the squared term: Divide each side by '-0.44'. -22.72727273 + -5.931818182x + x2 = 0 Move the constant term to the right: Add '22.72727273' to each side of the equation. -22.72727273 + -5.931818182x + 22.72727273 + x2 = 0 + 22.72727273 Reorder the terms: -22.72727273 + 22.72727273 + -5.931818182x + x2 = 0 + 22.72727273 Combine like terms: -22.72727273 + 22.72727273 = 0.00000000 0.00000000 + -5.931818182x + x2 = 0 + 22.72727273 -5.931818182x + x2 = 0 + 22.72727273 Combine like terms: 0 + 22.72727273 = 22.72727273 -5.931818182x + x2 = 22.72727273 The x term is -5.931818182x. Take half its coefficient (-2.965909091). Square it (8.796616736) and add it to both sides. Add '8.796616736' to each side of the equation. -5.931818182x + 8.796616736 + x2 = 22.72727273 + 8.796616736 Reorder the terms: 8.796616736 + -5.931818182x + x2 = 22.72727273 + 8.796616736 Combine like terms: 22.72727273 + 8.796616736 = 31.523889466 8.796616736 + -5.931818182x + x2 = 31.523889466 Factor a perfect square on the left side: (x + -2.965909091)(x + -2.965909091) = 31.523889466 Calculate the square root of the right side: 5.61461392 Break this problem into two subproblems by setting (x + -2.965909091) equal to 5.61461392 and -5.61461392.Subproblem 1
x + -2.965909091 = 5.61461392 Simplifying x + -2.965909091 = 5.61461392 Reorder the terms: -2.965909091 + x = 5.61461392 Solving -2.965909091 + x = 5.61461392 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.965909091' to each side of the equation. -2.965909091 + 2.965909091 + x = 5.61461392 + 2.965909091 Combine like terms: -2.965909091 + 2.965909091 = 0.000000000 0.000000000 + x = 5.61461392 + 2.965909091 x = 5.61461392 + 2.965909091 Combine like terms: 5.61461392 + 2.965909091 = 8.580523011 x = 8.580523011 Simplifying x = 8.580523011Subproblem 2
x + -2.965909091 = -5.61461392 Simplifying x + -2.965909091 = -5.61461392 Reorder the terms: -2.965909091 + x = -5.61461392 Solving -2.965909091 + x = -5.61461392 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.965909091' to each side of the equation. -2.965909091 + 2.965909091 + x = -5.61461392 + 2.965909091 Combine like terms: -2.965909091 + 2.965909091 = 0.000000000 0.000000000 + x = -5.61461392 + 2.965909091 x = -5.61461392 + 2.965909091 Combine like terms: -5.61461392 + 2.965909091 = -2.648704829 x = -2.648704829 Simplifying x = -2.648704829Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.580523011, -2.648704829}
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