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Simplifying 7.64x2 + 2.71x = 5.38 Reorder the terms: 2.71x + 7.64x2 = 5.38 Solving 2.71x + 7.64x2 = 5.38 Solving for variable 'x'. Reorder the terms: -5.38 + 2.71x + 7.64x2 = 5.38 + -5.38 Combine like terms: 5.38 + -5.38 = 0.00 -5.38 + 2.71x + 7.64x2 = 0.00 Begin completing the square. Divide all terms by 7.64 the coefficient of the squared term: Divide each side by '7.64'. -0.7041884817 + 0.3547120419x + x2 = 0 Move the constant term to the right: Add '0.7041884817' to each side of the equation. -0.7041884817 + 0.3547120419x + 0.7041884817 + x2 = 0 + 0.7041884817 Reorder the terms: -0.7041884817 + 0.7041884817 + 0.3547120419x + x2 = 0 + 0.7041884817 Combine like terms: -0.7041884817 + 0.7041884817 = 0.0000000000 0.0000000000 + 0.3547120419x + x2 = 0 + 0.7041884817 0.3547120419x + x2 = 0 + 0.7041884817 Combine like terms: 0 + 0.7041884817 = 0.7041884817 0.3547120419x + x2 = 0.7041884817 The x term is 0.3547120419x. Take half its coefficient (0.177356021). Square it (0.03145515819) and add it to both sides. Add '0.03145515819' to each side of the equation. 0.3547120419x + 0.03145515819 + x2 = 0.7041884817 + 0.03145515819 Reorder the terms: 0.03145515819 + 0.3547120419x + x2 = 0.7041884817 + 0.03145515819 Combine like terms: 0.7041884817 + 0.03145515819 = 0.73564363989 0.03145515819 + 0.3547120419x + x2 = 0.73564363989 Factor a perfect square on the left side: (x + 0.177356021)(x + 0.177356021) = 0.73564363989 Calculate the square root of the right side: 0.857696706 Break this problem into two subproblems by setting (x + 0.177356021) equal to 0.857696706 and -0.857696706.Subproblem 1
x + 0.177356021 = 0.857696706 Simplifying x + 0.177356021 = 0.857696706 Reorder the terms: 0.177356021 + x = 0.857696706 Solving 0.177356021 + x = 0.857696706 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.177356021' to each side of the equation. 0.177356021 + -0.177356021 + x = 0.857696706 + -0.177356021 Combine like terms: 0.177356021 + -0.177356021 = 0.000000000 0.000000000 + x = 0.857696706 + -0.177356021 x = 0.857696706 + -0.177356021 Combine like terms: 0.857696706 + -0.177356021 = 0.680340685 x = 0.680340685 Simplifying x = 0.680340685Subproblem 2
x + 0.177356021 = -0.857696706 Simplifying x + 0.177356021 = -0.857696706 Reorder the terms: 0.177356021 + x = -0.857696706 Solving 0.177356021 + x = -0.857696706 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.177356021' to each side of the equation. 0.177356021 + -0.177356021 + x = -0.857696706 + -0.177356021 Combine like terms: 0.177356021 + -0.177356021 = 0.000000000 0.000000000 + x = -0.857696706 + -0.177356021 x = -0.857696706 + -0.177356021 Combine like terms: -0.857696706 + -0.177356021 = -1.035052727 x = -1.035052727 Simplifying x = -1.035052727Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.680340685, -1.035052727}
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