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Simplifying 8x2 + 3.8x + -10.35 = 0 Reorder the terms: -10.35 + 3.8x + 8x2 = 0 Solving -10.35 + 3.8x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.29375 + 0.475x + x2 = 0 Move the constant term to the right: Add '1.29375' to each side of the equation. -1.29375 + 0.475x + 1.29375 + x2 = 0 + 1.29375 Reorder the terms: -1.29375 + 1.29375 + 0.475x + x2 = 0 + 1.29375 Combine like terms: -1.29375 + 1.29375 = 0.00000 0.00000 + 0.475x + x2 = 0 + 1.29375 0.475x + x2 = 0 + 1.29375 Combine like terms: 0 + 1.29375 = 1.29375 0.475x + x2 = 1.29375 The x term is 0.475x. Take half its coefficient (0.2375). Square it (0.05640625) and add it to both sides. Add '0.05640625' to each side of the equation. 0.475x + 0.05640625 + x2 = 1.29375 + 0.05640625 Reorder the terms: 0.05640625 + 0.475x + x2 = 1.29375 + 0.05640625 Combine like terms: 1.29375 + 0.05640625 = 1.35015625 0.05640625 + 0.475x + x2 = 1.35015625 Factor a perfect square on the left side: (x + 0.2375)(x + 0.2375) = 1.35015625 Calculate the square root of the right side: 1.161962241 Break this problem into two subproblems by setting (x + 0.2375) equal to 1.161962241 and -1.161962241.Subproblem 1
x + 0.2375 = 1.161962241 Simplifying x + 0.2375 = 1.161962241 Reorder the terms: 0.2375 + x = 1.161962241 Solving 0.2375 + x = 1.161962241 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2375' to each side of the equation. 0.2375 + -0.2375 + x = 1.161962241 + -0.2375 Combine like terms: 0.2375 + -0.2375 = 0.0000 0.0000 + x = 1.161962241 + -0.2375 x = 1.161962241 + -0.2375 Combine like terms: 1.161962241 + -0.2375 = 0.924462241 x = 0.924462241 Simplifying x = 0.924462241Subproblem 2
x + 0.2375 = -1.161962241 Simplifying x + 0.2375 = -1.161962241 Reorder the terms: 0.2375 + x = -1.161962241 Solving 0.2375 + x = -1.161962241 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2375' to each side of the equation. 0.2375 + -0.2375 + x = -1.161962241 + -0.2375 Combine like terms: 0.2375 + -0.2375 = 0.0000 0.0000 + x = -1.161962241 + -0.2375 x = -1.161962241 + -0.2375 Combine like terms: -1.161962241 + -0.2375 = -1.399462241 x = -1.399462241 Simplifying x = -1.399462241Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.924462241, -1.399462241}
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