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Simplifying 4.9x2 + -14x + -60 = 0 Reorder the terms: -60 + -14x + 4.9x2 = 0 Solving -60 + -14x + 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'. -12.24489796 + -2.857142857x + x2 = 0 Move the constant term to the right: Add '12.24489796' to each side of the equation. -12.24489796 + -2.857142857x + 12.24489796 + x2 = 0 + 12.24489796 Reorder the terms: -12.24489796 + 12.24489796 + -2.857142857x + x2 = 0 + 12.24489796 Combine like terms: -12.24489796 + 12.24489796 = 0.00000000 0.00000000 + -2.857142857x + x2 = 0 + 12.24489796 -2.857142857x + x2 = 0 + 12.24489796 Combine like terms: 0 + 12.24489796 = 12.24489796 -2.857142857x + x2 = 12.24489796 The x term is -2.857142857x. Take half its coefficient (-1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. -2.857142857x + 2.040816328 + x2 = 12.24489796 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857x + x2 = 12.24489796 + 2.040816328 Combine like terms: 12.24489796 + 2.040816328 = 14.285714288 2.040816328 + -2.857142857x + x2 = 14.285714288 Factor a perfect square on the left side: (x + -1.428571429)(x + -1.428571429) = 14.285714288 Calculate the square root of the right side: 3.77964473 Break this problem into two subproblems by setting (x + -1.428571429) equal to 3.77964473 and -3.77964473.Subproblem 1
x + -1.428571429 = 3.77964473 Simplifying x + -1.428571429 = 3.77964473 Reorder the terms: -1.428571429 + x = 3.77964473 Solving -1.428571429 + x = 3.77964473 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = 3.77964473 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = 3.77964473 + 1.428571429 x = 3.77964473 + 1.428571429 Combine like terms: 3.77964473 + 1.428571429 = 5.208216159 x = 5.208216159 Simplifying x = 5.208216159Subproblem 2
x + -1.428571429 = -3.77964473 Simplifying x + -1.428571429 = -3.77964473 Reorder the terms: -1.428571429 + x = -3.77964473 Solving -1.428571429 + x = -3.77964473 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = -3.77964473 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = -3.77964473 + 1.428571429 x = -3.77964473 + 1.428571429 Combine like terms: -3.77964473 + 1.428571429 = -2.351073301 x = -2.351073301 Simplifying x = -2.351073301Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.208216159, -2.351073301}
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