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Simplifying 11x2 + -2x + 9 = 62 Reorder the terms: 9 + -2x + 11x2 = 62 Solving 9 + -2x + 11x2 = 62 Solving for variable 'x'. Reorder the terms: 9 + -62 + -2x + 11x2 = 62 + -62 Combine like terms: 9 + -62 = -53 -53 + -2x + 11x2 = 62 + -62 Combine like terms: 62 + -62 = 0 -53 + -2x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -4.818181818 + -0.1818181818x + x2 = 0 Move the constant term to the right: Add '4.818181818' to each side of the equation. -4.818181818 + -0.1818181818x + 4.818181818 + x2 = 0 + 4.818181818 Reorder the terms: -4.818181818 + 4.818181818 + -0.1818181818x + x2 = 0 + 4.818181818 Combine like terms: -4.818181818 + 4.818181818 = 0.000000000 0.000000000 + -0.1818181818x + x2 = 0 + 4.818181818 -0.1818181818x + x2 = 0 + 4.818181818 Combine like terms: 0 + 4.818181818 = 4.818181818 -0.1818181818x + x2 = 4.818181818 The x term is -0.1818181818x. Take half its coefficient (-0.0909090909). Square it (0.008264462808) and add it to both sides. Add '0.008264462808' to each side of the equation. -0.1818181818x + 0.008264462808 + x2 = 4.818181818 + 0.008264462808 Reorder the terms: 0.008264462808 + -0.1818181818x + x2 = 4.818181818 + 0.008264462808 Combine like terms: 4.818181818 + 0.008264462808 = 4.826446280808 0.008264462808 + -0.1818181818x + x2 = 4.826446280808 Factor a perfect square on the left side: (x + -0.0909090909)(x + -0.0909090909) = 4.826446280808 Calculate the square root of the right side: 2.19691745 Break this problem into two subproblems by setting (x + -0.0909090909) equal to 2.19691745 and -2.19691745.Subproblem 1
x + -0.0909090909 = 2.19691745 Simplifying x + -0.0909090909 = 2.19691745 Reorder the terms: -0.0909090909 + x = 2.19691745 Solving -0.0909090909 + x = 2.19691745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0909090909' to each side of the equation. -0.0909090909 + 0.0909090909 + x = 2.19691745 + 0.0909090909 Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000 0.0000000000 + x = 2.19691745 + 0.0909090909 x = 2.19691745 + 0.0909090909 Combine like terms: 2.19691745 + 0.0909090909 = 2.2878265409 x = 2.2878265409 Simplifying x = 2.2878265409Subproblem 2
x + -0.0909090909 = -2.19691745 Simplifying x + -0.0909090909 = -2.19691745 Reorder the terms: -0.0909090909 + x = -2.19691745 Solving -0.0909090909 + x = -2.19691745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0909090909' to each side of the equation. -0.0909090909 + 0.0909090909 + x = -2.19691745 + 0.0909090909 Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000 0.0000000000 + x = -2.19691745 + 0.0909090909 x = -2.19691745 + 0.0909090909 Combine like terms: -2.19691745 + 0.0909090909 = -2.1060083591 x = -2.1060083591 Simplifying x = -2.1060083591Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2878265409, -2.1060083591}
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