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Simplifying 110x2 + 21x + -271 = 320 Reorder the terms: -271 + 21x + 110x2 = 320 Solving -271 + 21x + 110x2 = 320 Solving for variable 'x'. Reorder the terms: -271 + -320 + 21x + 110x2 = 320 + -320 Combine like terms: -271 + -320 = -591 -591 + 21x + 110x2 = 320 + -320 Combine like terms: 320 + -320 = 0 -591 + 21x + 110x2 = 0 Begin completing the square. Divide all terms by 110 the coefficient of the squared term: Divide each side by '110'. -5.372727273 + 0.1909090909x + x2 = 0 Move the constant term to the right: Add '5.372727273' to each side of the equation. -5.372727273 + 0.1909090909x + 5.372727273 + x2 = 0 + 5.372727273 Reorder the terms: -5.372727273 + 5.372727273 + 0.1909090909x + x2 = 0 + 5.372727273 Combine like terms: -5.372727273 + 5.372727273 = 0.000000000 0.000000000 + 0.1909090909x + x2 = 0 + 5.372727273 0.1909090909x + x2 = 0 + 5.372727273 Combine like terms: 0 + 5.372727273 = 5.372727273 0.1909090909x + x2 = 5.372727273 The x term is 0.1909090909x. Take half its coefficient (0.09545454545). Square it (0.009111570247) and add it to both sides. Add '0.009111570247' to each side of the equation. 0.1909090909x + 0.009111570247 + x2 = 5.372727273 + 0.009111570247 Reorder the terms: 0.009111570247 + 0.1909090909x + x2 = 5.372727273 + 0.009111570247 Combine like terms: 5.372727273 + 0.009111570247 = 5.381838843247 0.009111570247 + 0.1909090909x + x2 = 5.381838843247 Factor a perfect square on the left side: (x + 0.09545454545)(x + 0.09545454545) = 5.381838843247 Calculate the square root of the right side: 2.319879058 Break this problem into two subproblems by setting (x + 0.09545454545) equal to 2.319879058 and -2.319879058.Subproblem 1
x + 0.09545454545 = 2.319879058 Simplifying x + 0.09545454545 = 2.319879058 Reorder the terms: 0.09545454545 + x = 2.319879058 Solving 0.09545454545 + x = 2.319879058 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.09545454545' to each side of the equation. 0.09545454545 + -0.09545454545 + x = 2.319879058 + -0.09545454545 Combine like terms: 0.09545454545 + -0.09545454545 = 0.00000000000 0.00000000000 + x = 2.319879058 + -0.09545454545 x = 2.319879058 + -0.09545454545 Combine like terms: 2.319879058 + -0.09545454545 = 2.22442451255 x = 2.22442451255 Simplifying x = 2.22442451255Subproblem 2
x + 0.09545454545 = -2.319879058 Simplifying x + 0.09545454545 = -2.319879058 Reorder the terms: 0.09545454545 + x = -2.319879058 Solving 0.09545454545 + x = -2.319879058 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.09545454545' to each side of the equation. 0.09545454545 + -0.09545454545 + x = -2.319879058 + -0.09545454545 Combine like terms: 0.09545454545 + -0.09545454545 = 0.00000000000 0.00000000000 + x = -2.319879058 + -0.09545454545 x = -2.319879058 + -0.09545454545 Combine like terms: -2.319879058 + -0.09545454545 = -2.41533360345 x = -2.41533360345 Simplifying x = -2.41533360345Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.22442451255, -2.41533360345}
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