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Simplifying 110x2 + -193x + 78 = 0 Reorder the terms: 78 + -193x + 110x2 = 0 Solving 78 + -193x + 110x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 110 the coefficient of the squared term: Divide each side by '110'. 0.7090909091 + -1.754545455x + x2 = 0 Move the constant term to the right: Add '-0.7090909091' to each side of the equation. 0.7090909091 + -1.754545455x + -0.7090909091 + x2 = 0 + -0.7090909091 Reorder the terms: 0.7090909091 + -0.7090909091 + -1.754545455x + x2 = 0 + -0.7090909091 Combine like terms: 0.7090909091 + -0.7090909091 = 0.0000000000 0.0000000000 + -1.754545455x + x2 = 0 + -0.7090909091 -1.754545455x + x2 = 0 + -0.7090909091 Combine like terms: 0 + -0.7090909091 = -0.7090909091 -1.754545455x + x2 = -0.7090909091 The x term is -1.754545455x. Take half its coefficient (-0.8772727275). Square it (0.7696074384) and add it to both sides. Add '0.7696074384' to each side of the equation. -1.754545455x + 0.7696074384 + x2 = -0.7090909091 + 0.7696074384 Reorder the terms: 0.7696074384 + -1.754545455x + x2 = -0.7090909091 + 0.7696074384 Combine like terms: -0.7090909091 + 0.7696074384 = 0.0605165293 0.7696074384 + -1.754545455x + x2 = 0.0605165293 Factor a perfect square on the left side: (x + -0.8772727275)(x + -0.8772727275) = 0.0605165293 Calculate the square root of the right side: 0.246001076 Break this problem into two subproblems by setting (x + -0.8772727275) equal to 0.246001076 and -0.246001076.Subproblem 1
x + -0.8772727275 = 0.246001076 Simplifying x + -0.8772727275 = 0.246001076 Reorder the terms: -0.8772727275 + x = 0.246001076 Solving -0.8772727275 + x = 0.246001076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8772727275' to each side of the equation. -0.8772727275 + 0.8772727275 + x = 0.246001076 + 0.8772727275 Combine like terms: -0.8772727275 + 0.8772727275 = 0.0000000000 0.0000000000 + x = 0.246001076 + 0.8772727275 x = 0.246001076 + 0.8772727275 Combine like terms: 0.246001076 + 0.8772727275 = 1.1232738035 x = 1.1232738035 Simplifying x = 1.1232738035Subproblem 2
x + -0.8772727275 = -0.246001076 Simplifying x + -0.8772727275 = -0.246001076 Reorder the terms: -0.8772727275 + x = -0.246001076 Solving -0.8772727275 + x = -0.246001076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8772727275' to each side of the equation. -0.8772727275 + 0.8772727275 + x = -0.246001076 + 0.8772727275 Combine like terms: -0.8772727275 + 0.8772727275 = 0.0000000000 0.0000000000 + x = -0.246001076 + 0.8772727275 x = -0.246001076 + 0.8772727275 Combine like terms: -0.246001076 + 0.8772727275 = 0.6312716515 x = 0.6312716515 Simplifying x = 0.6312716515Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1232738035, 0.6312716515}
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