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Simplifying 0 = -50 + 31.304x + 4.9x2 Solving 0 = -50 + 31.304x + 4.9x2 Solving for variable 'x'. Combine like terms: 0 + 50 = 50 50 + -31.304x + -4.9x2 = -50 + 31.304x + 4.9x2 + 50 + -31.304x + -4.9x2 Reorder the terms: 50 + -31.304x + -4.9x2 = -50 + 50 + 31.304x + -31.304x + 4.9x2 + -4.9x2 Combine like terms: -50 + 50 = 0 50 + -31.304x + -4.9x2 = 0 + 31.304x + -31.304x + 4.9x2 + -4.9x2 50 + -31.304x + -4.9x2 = 31.304x + -31.304x + 4.9x2 + -4.9x2 Combine like terms: 31.304x + -31.304x = 0.000 50 + -31.304x + -4.9x2 = 0.000 + 4.9x2 + -4.9x2 50 + -31.304x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 50 + -31.304x + -4.9x2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -10.20408163 + 6.388571429x + x2 = 0 Move the constant term to the right: Add '10.20408163' to each side of the equation. -10.20408163 + 6.388571429x + 10.20408163 + x2 = 0 + 10.20408163 Reorder the terms: -10.20408163 + 10.20408163 + 6.388571429x + x2 = 0 + 10.20408163 Combine like terms: -10.20408163 + 10.20408163 = 0.00000000 0.00000000 + 6.388571429x + x2 = 0 + 10.20408163 6.388571429x + x2 = 0 + 10.20408163 Combine like terms: 0 + 10.20408163 = 10.20408163 6.388571429x + x2 = 10.20408163 The x term is 6.388571429x. Take half its coefficient (3.194285715). Square it (10.20346123) and add it to both sides. Add '10.20346123' to each side of the equation. 6.388571429x + 10.20346123 + x2 = 10.20408163 + 10.20346123 Reorder the terms: 10.20346123 + 6.388571429x + x2 = 10.20408163 + 10.20346123 Combine like terms: 10.20408163 + 10.20346123 = 20.40754286 10.20346123 + 6.388571429x + x2 = 20.40754286 Factor a perfect square on the left side: (x + 3.194285715)(x + 3.194285715) = 20.40754286 Calculate the square root of the right side: 4.517470848 Break this problem into two subproblems by setting (x + 3.194285715) equal to 4.517470848 and -4.517470848.Subproblem 1
x + 3.194285715 = 4.517470848 Simplifying x + 3.194285715 = 4.517470848 Reorder the terms: 3.194285715 + x = 4.517470848 Solving 3.194285715 + x = 4.517470848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.194285715' to each side of the equation. 3.194285715 + -3.194285715 + x = 4.517470848 + -3.194285715 Combine like terms: 3.194285715 + -3.194285715 = 0.000000000 0.000000000 + x = 4.517470848 + -3.194285715 x = 4.517470848 + -3.194285715 Combine like terms: 4.517470848 + -3.194285715 = 1.323185133 x = 1.323185133 Simplifying x = 1.323185133Subproblem 2
x + 3.194285715 = -4.517470848 Simplifying x + 3.194285715 = -4.517470848 Reorder the terms: 3.194285715 + x = -4.517470848 Solving 3.194285715 + x = -4.517470848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.194285715' to each side of the equation. 3.194285715 + -3.194285715 + x = -4.517470848 + -3.194285715 Combine like terms: 3.194285715 + -3.194285715 = 0.000000000 0.000000000 + x = -4.517470848 + -3.194285715 x = -4.517470848 + -3.194285715 Combine like terms: -4.517470848 + -3.194285715 = -7.711756563 x = -7.711756563 Simplifying x = -7.711756563Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.323185133, -7.711756563}
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