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Simplifying (-4.9x2) + -7x + 450 = 0 Reorder the terms: 450 + -7x + (-4.9x2) = 0 Solving 450 + -7x + (-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'. -91.83673469 + 1.428571429x + x2 = 0 Move the constant term to the right: Add '91.83673469' to each side of the equation. -91.83673469 + 1.428571429x + 91.83673469 + x2 = 0 + 91.83673469 Reorder the terms: -91.83673469 + 91.83673469 + 1.428571429x + x2 = 0 + 91.83673469 Combine like terms: -91.83673469 + 91.83673469 = 0.00000000 0.00000000 + 1.428571429x + x2 = 0 + 91.83673469 1.428571429x + x2 = 0 + 91.83673469 Combine like terms: 0 + 91.83673469 = 91.83673469 1.428571429x + x2 = 91.83673469 The x term is 1.428571429x. Take half its coefficient (0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. 1.428571429x + 0.5102040819 + x2 = 91.83673469 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429x + x2 = 91.83673469 + 0.5102040819 Combine like terms: 91.83673469 + 0.5102040819 = 92.3469387719 0.5102040819 + 1.428571429x + x2 = 92.3469387719 Factor a perfect square on the left side: ((x) + 0.7142857145)((x) + 0.7142857145) = 92.3469387719 Calculate the square root of the right side: 9.609731462 Break this problem into two subproblems by setting ((x) + 0.7142857145) equal to 9.609731462 and -9.609731462.Subproblem 1
(x) + 0.7142857145 = 9.609731462 Simplifying (x) + 0.7142857145 = 9.609731462 x + 0.7142857145 = 9.609731462 Reorder the terms: 0.7142857145 + x = 9.609731462 Solving 0.7142857145 + x = 9.609731462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + x = 9.609731462 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = 9.609731462 + -0.7142857145 x = 9.609731462 + -0.7142857145 Combine like terms: 9.609731462 + -0.7142857145 = 8.8954457475 x = 8.8954457475 Simplifying x = 8.8954457475Subproblem 2
(x) + 0.7142857145 = -9.609731462 Simplifying (x) + 0.7142857145 = -9.609731462 x + 0.7142857145 = -9.609731462 Reorder the terms: 0.7142857145 + x = -9.609731462 Solving 0.7142857145 + x = -9.609731462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + x = -9.609731462 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = -9.609731462 + -0.7142857145 x = -9.609731462 + -0.7142857145 Combine like terms: -9.609731462 + -0.7142857145 = -10.3240171765 x = -10.3240171765 Simplifying x = -10.3240171765Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.8954457475, -10.3240171765}
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