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Simplifying 7.61x2 + 2.77x + -5.33 = 0 Reorder the terms: -5.33 + 2.77x + 7.61x2 = 0 Solving -5.33 + 2.77x + 7.61x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7.61 the coefficient of the squared term: Divide each side by '7.61'. -0.7003942181 + 0.3639947438x + x2 = 0 Move the constant term to the right: Add '0.7003942181' to each side of the equation. -0.7003942181 + 0.3639947438x + 0.7003942181 + x2 = 0 + 0.7003942181 Reorder the terms: -0.7003942181 + 0.7003942181 + 0.3639947438x + x2 = 0 + 0.7003942181 Combine like terms: -0.7003942181 + 0.7003942181 = 0.0000000000 0.0000000000 + 0.3639947438x + x2 = 0 + 0.7003942181 0.3639947438x + x2 = 0 + 0.7003942181 Combine like terms: 0 + 0.7003942181 = 0.7003942181 0.3639947438x + x2 = 0.7003942181 The x term is 0.3639947438x. Take half its coefficient (0.1819973719). Square it (0.03312304338) and add it to both sides. Add '0.03312304338' to each side of the equation. 0.3639947438x + 0.03312304338 + x2 = 0.7003942181 + 0.03312304338 Reorder the terms: 0.03312304338 + 0.3639947438x + x2 = 0.7003942181 + 0.03312304338 Combine like terms: 0.7003942181 + 0.03312304338 = 0.73351726148 0.03312304338 + 0.3639947438x + x2 = 0.73351726148 Factor a perfect square on the left side: (x + 0.1819973719)(x + 0.1819973719) = 0.73351726148 Calculate the square root of the right side: 0.856456223 Break this problem into two subproblems by setting (x + 0.1819973719) equal to 0.856456223 and -0.856456223.Subproblem 1
x + 0.1819973719 = 0.856456223 Simplifying x + 0.1819973719 = 0.856456223 Reorder the terms: 0.1819973719 + x = 0.856456223 Solving 0.1819973719 + x = 0.856456223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1819973719' to each side of the equation. 0.1819973719 + -0.1819973719 + x = 0.856456223 + -0.1819973719 Combine like terms: 0.1819973719 + -0.1819973719 = 0.0000000000 0.0000000000 + x = 0.856456223 + -0.1819973719 x = 0.856456223 + -0.1819973719 Combine like terms: 0.856456223 + -0.1819973719 = 0.6744588511 x = 0.6744588511 Simplifying x = 0.6744588511Subproblem 2
x + 0.1819973719 = -0.856456223 Simplifying x + 0.1819973719 = -0.856456223 Reorder the terms: 0.1819973719 + x = -0.856456223 Solving 0.1819973719 + x = -0.856456223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1819973719' to each side of the equation. 0.1819973719 + -0.1819973719 + x = -0.856456223 + -0.1819973719 Combine like terms: 0.1819973719 + -0.1819973719 = 0.0000000000 0.0000000000 + x = -0.856456223 + -0.1819973719 x = -0.856456223 + -0.1819973719 Combine like terms: -0.856456223 + -0.1819973719 = -1.0384535949 x = -1.0384535949 Simplifying x = -1.0384535949Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6744588511, -1.0384535949}
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