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Simplifying 14x2 + 35x + -20 = 0 Reorder the terms: -20 + 35x + 14x2 = 0 Solving -20 + 35x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -1.428571429 + 2.5x + x2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + 2.5x + 1.428571429 + x2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + 2.5x + x2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + 2.5x + x2 = 0 + 1.428571429 2.5x + x2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 2.5x + x2 = 1.428571429 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 1.428571429 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 1.428571429 + 1.5625 Combine like terms: 1.428571429 + 1.5625 = 2.991071429 1.5625 + 2.5x + x2 = 2.991071429 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 2.991071429 Calculate the square root of the right side: 1.729471431 Break this problem into two subproblems by setting (x + 1.25) equal to 1.729471431 and -1.729471431.Subproblem 1
x + 1.25 = 1.729471431 Simplifying x + 1.25 = 1.729471431 Reorder the terms: 1.25 + x = 1.729471431 Solving 1.25 + x = 1.729471431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 1.729471431 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.729471431 + -1.25 x = 1.729471431 + -1.25 Combine like terms: 1.729471431 + -1.25 = 0.479471431 x = 0.479471431 Simplifying x = 0.479471431Subproblem 2
x + 1.25 = -1.729471431 Simplifying x + 1.25 = -1.729471431 Reorder the terms: 1.25 + x = -1.729471431 Solving 1.25 + x = -1.729471431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -1.729471431 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.729471431 + -1.25 x = -1.729471431 + -1.25 Combine like terms: -1.729471431 + -1.25 = -2.979471431 x = -2.979471431 Simplifying x = -2.979471431Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.479471431, -2.979471431}
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