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Simplifying -4.9x2 + 34.3x + -58.0 = 0 Reorder the terms: -58.0 + 34.3x + -4.9x2 = 0 Solving -58.0 + 34.3x + -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'. 11.83673469 + -7x + x2 = 0 Move the constant term to the right: Add '-11.83673469' to each side of the equation. 11.83673469 + -7x + -11.83673469 + x2 = 0 + -11.83673469 Reorder the terms: 11.83673469 + -11.83673469 + -7x + x2 = 0 + -11.83673469 Combine like terms: 11.83673469 + -11.83673469 = 0.00000000 0.00000000 + -7x + x2 = 0 + -11.83673469 -7x + x2 = 0 + -11.83673469 Combine like terms: 0 + -11.83673469 = -11.83673469 -7x + x2 = -11.83673469 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -11.83673469 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -11.83673469 + 12.25 Combine like terms: -11.83673469 + 12.25 = 0.41326531 12.25 + -7x + x2 = 0.41326531 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 0.41326531 Calculate the square root of the right side: 0.642857146 Break this problem into two subproblems by setting (x + -3.5) equal to 0.642857146 and -0.642857146.Subproblem 1
x + -3.5 = 0.642857146 Simplifying x + -3.5 = 0.642857146 Reorder the terms: -3.5 + x = 0.642857146 Solving -3.5 + x = 0.642857146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 0.642857146 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 0.642857146 + 3.5 x = 0.642857146 + 3.5 Combine like terms: 0.642857146 + 3.5 = 4.142857146 x = 4.142857146 Simplifying x = 4.142857146Subproblem 2
x + -3.5 = -0.642857146 Simplifying x + -3.5 = -0.642857146 Reorder the terms: -3.5 + x = -0.642857146 Solving -3.5 + x = -0.642857146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -0.642857146 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -0.642857146 + 3.5 x = -0.642857146 + 3.5 Combine like terms: -0.642857146 + 3.5 = 2.857142854 x = 2.857142854 Simplifying x = 2.857142854Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.142857146, 2.857142854}
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