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Simplifying 22x2 + 61x + -30 = 0 Reorder the terms: -30 + 61x + 22x2 = 0 Solving -30 + 61x + 22x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 22 the coefficient of the squared term: Divide each side by '22'. -1.363636364 + 2.772727273x + x2 = 0 Move the constant term to the right: Add '1.363636364' to each side of the equation. -1.363636364 + 2.772727273x + 1.363636364 + x2 = 0 + 1.363636364 Reorder the terms: -1.363636364 + 1.363636364 + 2.772727273x + x2 = 0 + 1.363636364 Combine like terms: -1.363636364 + 1.363636364 = 0.000000000 0.000000000 + 2.772727273x + x2 = 0 + 1.363636364 2.772727273x + x2 = 0 + 1.363636364 Combine like terms: 0 + 1.363636364 = 1.363636364 2.772727273x + x2 = 1.363636364 The x term is 2.772727273x. Take half its coefficient (1.386363637). Square it (1.922004134) and add it to both sides. Add '1.922004134' to each side of the equation. 2.772727273x + 1.922004134 + x2 = 1.363636364 + 1.922004134 Reorder the terms: 1.922004134 + 2.772727273x + x2 = 1.363636364 + 1.922004134 Combine like terms: 1.363636364 + 1.922004134 = 3.285640498 1.922004134 + 2.772727273x + x2 = 3.285640498 Factor a perfect square on the left side: (x + 1.386363637)(x + 1.386363637) = 3.285640498 Calculate the square root of the right side: 1.812633581 Break this problem into two subproblems by setting (x + 1.386363637) equal to 1.812633581 and -1.812633581.Subproblem 1
x + 1.386363637 = 1.812633581 Simplifying x + 1.386363637 = 1.812633581 Reorder the terms: 1.386363637 + x = 1.812633581 Solving 1.386363637 + x = 1.812633581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.386363637' to each side of the equation. 1.386363637 + -1.386363637 + x = 1.812633581 + -1.386363637 Combine like terms: 1.386363637 + -1.386363637 = 0.000000000 0.000000000 + x = 1.812633581 + -1.386363637 x = 1.812633581 + -1.386363637 Combine like terms: 1.812633581 + -1.386363637 = 0.426269944 x = 0.426269944 Simplifying x = 0.426269944Subproblem 2
x + 1.386363637 = -1.812633581 Simplifying x + 1.386363637 = -1.812633581 Reorder the terms: 1.386363637 + x = -1.812633581 Solving 1.386363637 + x = -1.812633581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.386363637' to each side of the equation. 1.386363637 + -1.386363637 + x = -1.812633581 + -1.386363637 Combine like terms: 1.386363637 + -1.386363637 = 0.000000000 0.000000000 + x = -1.812633581 + -1.386363637 x = -1.812633581 + -1.386363637 Combine like terms: -1.812633581 + -1.386363637 = -3.198997218 x = -3.198997218 Simplifying x = -3.198997218Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.426269944, -3.198997218}
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