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Simplifying 4.9x2 + -343x + -27 = 0 Reorder the terms: -27 + -343x + 4.9x2 = 0 Solving -27 + -343x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -5.510204082 + -70x + x2 = 0 Move the constant term to the right: Add '5.510204082' to each side of the equation. -5.510204082 + -70x + 5.510204082 + x2 = 0 + 5.510204082 Reorder the terms: -5.510204082 + 5.510204082 + -70x + x2 = 0 + 5.510204082 Combine like terms: -5.510204082 + 5.510204082 = 0.000000000 0.000000000 + -70x + x2 = 0 + 5.510204082 -70x + x2 = 0 + 5.510204082 Combine like terms: 0 + 5.510204082 = 5.510204082 -70x + x2 = 5.510204082 The x term is -70x. Take half its coefficient (-35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. -70x + 1225 + x2 = 5.510204082 + 1225 Reorder the terms: 1225 + -70x + x2 = 5.510204082 + 1225 Combine like terms: 5.510204082 + 1225 = 1230.510204082 1225 + -70x + x2 = 1230.510204082 Factor a perfect square on the left side: (x + -35)(x + -35) = 1230.510204082 Calculate the square root of the right side: 35.07862888 Break this problem into two subproblems by setting (x + -35) equal to 35.07862888 and -35.07862888.Subproblem 1
x + -35 = 35.07862888 Simplifying x + -35 = 35.07862888 Reorder the terms: -35 + x = 35.07862888 Solving -35 + x = 35.07862888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + x = 35.07862888 + 35 Combine like terms: -35 + 35 = 0 0 + x = 35.07862888 + 35 x = 35.07862888 + 35 Combine like terms: 35.07862888 + 35 = 70.07862888 x = 70.07862888 Simplifying x = 70.07862888Subproblem 2
x + -35 = -35.07862888 Simplifying x + -35 = -35.07862888 Reorder the terms: -35 + x = -35.07862888 Solving -35 + x = -35.07862888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + x = -35.07862888 + 35 Combine like terms: -35 + 35 = 0 0 + x = -35.07862888 + 35 x = -35.07862888 + 35 Combine like terms: -35.07862888 + 35 = -0.07862888 x = -0.07862888 Simplifying x = -0.07862888Solution
The solution to the problem is based on the solutions from the subproblems. x = {70.07862888, -0.07862888}
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