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Simplifying 10x2 + -27x + 18.22 = 0 Reorder the terms: 18.22 + -27x + 10x2 = 0 Solving 18.22 + -27x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1.822 + -2.7x + x2 = 0 Move the constant term to the right: Add '-1.822' to each side of the equation. 1.822 + -2.7x + -1.822 + x2 = 0 + -1.822 Reorder the terms: 1.822 + -1.822 + -2.7x + x2 = 0 + -1.822 Combine like terms: 1.822 + -1.822 = 0.000 0.000 + -2.7x + x2 = 0 + -1.822 -2.7x + x2 = 0 + -1.822 Combine like terms: 0 + -1.822 = -1.822 -2.7x + x2 = -1.822 The x term is -2.7x. Take half its coefficient (-1.35). Square it (1.8225) and add it to both sides. Add '1.8225' to each side of the equation. -2.7x + 1.8225 + x2 = -1.822 + 1.8225 Reorder the terms: 1.8225 + -2.7x + x2 = -1.822 + 1.8225 Combine like terms: -1.822 + 1.8225 = 0.0005 1.8225 + -2.7x + x2 = 0.0005 Factor a perfect square on the left side: (x + -1.35)(x + -1.35) = 0.0005 Calculate the square root of the right side: 0.02236068 Break this problem into two subproblems by setting (x + -1.35) equal to 0.02236068 and -0.02236068.Subproblem 1
x + -1.35 = 0.02236068 Simplifying x + -1.35 = 0.02236068 Reorder the terms: -1.35 + x = 0.02236068 Solving -1.35 + x = 0.02236068 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.35' to each side of the equation. -1.35 + 1.35 + x = 0.02236068 + 1.35 Combine like terms: -1.35 + 1.35 = 0.00 0.00 + x = 0.02236068 + 1.35 x = 0.02236068 + 1.35 Combine like terms: 0.02236068 + 1.35 = 1.37236068 x = 1.37236068 Simplifying x = 1.37236068Subproblem 2
x + -1.35 = -0.02236068 Simplifying x + -1.35 = -0.02236068 Reorder the terms: -1.35 + x = -0.02236068 Solving -1.35 + x = -0.02236068 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.35' to each side of the equation. -1.35 + 1.35 + x = -0.02236068 + 1.35 Combine like terms: -1.35 + 1.35 = 0.00 0.00 + x = -0.02236068 + 1.35 x = -0.02236068 + 1.35 Combine like terms: -0.02236068 + 1.35 = 1.32763932 x = 1.32763932 Simplifying x = 1.32763932Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.37236068, 1.32763932}
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