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Simplifying 8.14x2 + 3.88x = 5.85 Reorder the terms: 3.88x + 8.14x2 = 5.85 Solving 3.88x + 8.14x2 = 5.85 Solving for variable 'x'. Reorder the terms: -5.85 + 3.88x + 8.14x2 = 5.85 + -5.85 Combine like terms: 5.85 + -5.85 = 0.00 -5.85 + 3.88x + 8.14x2 = 0.00 Begin completing the square. Divide all terms by 8.14 the coefficient of the squared term: Divide each side by '8.14'. -0.7186732187 + 0.4766584767x + x2 = 0 Move the constant term to the right: Add '0.7186732187' to each side of the equation. -0.7186732187 + 0.4766584767x + 0.7186732187 + x2 = 0 + 0.7186732187 Reorder the terms: -0.7186732187 + 0.7186732187 + 0.4766584767x + x2 = 0 + 0.7186732187 Combine like terms: -0.7186732187 + 0.7186732187 = 0.0000000000 0.0000000000 + 0.4766584767x + x2 = 0 + 0.7186732187 0.4766584767x + x2 = 0 + 0.7186732187 Combine like terms: 0 + 0.7186732187 = 0.7186732187 0.4766584767x + x2 = 0.7186732187 The x term is 0.4766584767x. Take half its coefficient (0.2383292384). Square it (0.05680082588) and add it to both sides. Add '0.05680082588' to each side of the equation. 0.4766584767x + 0.05680082588 + x2 = 0.7186732187 + 0.05680082588 Reorder the terms: 0.05680082588 + 0.4766584767x + x2 = 0.7186732187 + 0.05680082588 Combine like terms: 0.7186732187 + 0.05680082588 = 0.77547404458 0.05680082588 + 0.4766584767x + x2 = 0.77547404458 Factor a perfect square on the left side: (x + 0.2383292384)(x + 0.2383292384) = 0.77547404458 Calculate the square root of the right side: 0.880610041 Break this problem into two subproblems by setting (x + 0.2383292384) equal to 0.880610041 and -0.880610041.Subproblem 1
x + 0.2383292384 = 0.880610041 Simplifying x + 0.2383292384 = 0.880610041 Reorder the terms: 0.2383292384 + x = 0.880610041 Solving 0.2383292384 + x = 0.880610041 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2383292384' to each side of the equation. 0.2383292384 + -0.2383292384 + x = 0.880610041 + -0.2383292384 Combine like terms: 0.2383292384 + -0.2383292384 = 0.0000000000 0.0000000000 + x = 0.880610041 + -0.2383292384 x = 0.880610041 + -0.2383292384 Combine like terms: 0.880610041 + -0.2383292384 = 0.6422808026 x = 0.6422808026 Simplifying x = 0.6422808026Subproblem 2
x + 0.2383292384 = -0.880610041 Simplifying x + 0.2383292384 = -0.880610041 Reorder the terms: 0.2383292384 + x = -0.880610041 Solving 0.2383292384 + x = -0.880610041 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2383292384' to each side of the equation. 0.2383292384 + -0.2383292384 + x = -0.880610041 + -0.2383292384 Combine like terms: 0.2383292384 + -0.2383292384 = 0.0000000000 0.0000000000 + x = -0.880610041 + -0.2383292384 x = -0.880610041 + -0.2383292384 Combine like terms: -0.880610041 + -0.2383292384 = -1.1189392794 x = -1.1189392794 Simplifying x = -1.1189392794Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6422808026, -1.1189392794}
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