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Simplifying 7.69x2 + 2.78x = 5.37 Reorder the terms: 2.78x + 7.69x2 = 5.37 Solving 2.78x + 7.69x2 = 5.37 Solving for variable 'x'. Reorder the terms: -5.37 + 2.78x + 7.69x2 = 5.37 + -5.37 Combine like terms: 5.37 + -5.37 = 0.00 -5.37 + 2.78x + 7.69x2 = 0.00 Begin completing the square. Divide all terms by 7.69 the coefficient of the squared term: Divide each side by '7.69'. -0.6983094928 + 0.3615084525x + x2 = 0 Move the constant term to the right: Add '0.6983094928' to each side of the equation. -0.6983094928 + 0.3615084525x + 0.6983094928 + x2 = 0 + 0.6983094928 Reorder the terms: -0.6983094928 + 0.6983094928 + 0.3615084525x + x2 = 0 + 0.6983094928 Combine like terms: -0.6983094928 + 0.6983094928 = 0.0000000000 0.0000000000 + 0.3615084525x + x2 = 0 + 0.6983094928 0.3615084525x + x2 = 0 + 0.6983094928 Combine like terms: 0 + 0.6983094928 = 0.6983094928 0.3615084525x + x2 = 0.6983094928 The x term is 0.3615084525x. Take half its coefficient (0.1807542263). Square it (0.03267209033) and add it to both sides. Add '0.03267209033' to each side of the equation. 0.3615084525x + 0.03267209033 + x2 = 0.6983094928 + 0.03267209033 Reorder the terms: 0.03267209033 + 0.3615084525x + x2 = 0.6983094928 + 0.03267209033 Combine like terms: 0.6983094928 + 0.03267209033 = 0.73098158313 0.03267209033 + 0.3615084525x + x2 = 0.73098158313 Factor a perfect square on the left side: (x + 0.1807542263)(x + 0.1807542263) = 0.73098158313 Calculate the square root of the right side: 0.85497461 Break this problem into two subproblems by setting (x + 0.1807542263) equal to 0.85497461 and -0.85497461.Subproblem 1
x + 0.1807542263 = 0.85497461 Simplifying x + 0.1807542263 = 0.85497461 Reorder the terms: 0.1807542263 + x = 0.85497461 Solving 0.1807542263 + x = 0.85497461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1807542263' to each side of the equation. 0.1807542263 + -0.1807542263 + x = 0.85497461 + -0.1807542263 Combine like terms: 0.1807542263 + -0.1807542263 = 0.0000000000 0.0000000000 + x = 0.85497461 + -0.1807542263 x = 0.85497461 + -0.1807542263 Combine like terms: 0.85497461 + -0.1807542263 = 0.6742203837 x = 0.6742203837 Simplifying x = 0.6742203837Subproblem 2
x + 0.1807542263 = -0.85497461 Simplifying x + 0.1807542263 = -0.85497461 Reorder the terms: 0.1807542263 + x = -0.85497461 Solving 0.1807542263 + x = -0.85497461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1807542263' to each side of the equation. 0.1807542263 + -0.1807542263 + x = -0.85497461 + -0.1807542263 Combine like terms: 0.1807542263 + -0.1807542263 = 0.0000000000 0.0000000000 + x = -0.85497461 + -0.1807542263 x = -0.85497461 + -0.1807542263 Combine like terms: -0.85497461 + -0.1807542263 = -1.0357288363 x = -1.0357288363 Simplifying x = -1.0357288363Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6742203837, -1.0357288363}
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