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Simplifying 0.72x2 + -30.5x + 68 = 0 Reorder the terms: 68 + -30.5x + 0.72x2 = 0 Solving 68 + -30.5x + 0.72x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.72 the coefficient of the squared term: Divide each side by '0.72'. 94.44444444 + -42.36111111x + x2 = 0 Move the constant term to the right: Add '-94.44444444' to each side of the equation. 94.44444444 + -42.36111111x + -94.44444444 + x2 = 0 + -94.44444444 Reorder the terms: 94.44444444 + -94.44444444 + -42.36111111x + x2 = 0 + -94.44444444 Combine like terms: 94.44444444 + -94.44444444 = 0.00000000 0.00000000 + -42.36111111x + x2 = 0 + -94.44444444 -42.36111111x + x2 = 0 + -94.44444444 Combine like terms: 0 + -94.44444444 = -94.44444444 -42.36111111x + x2 = -94.44444444 The x term is -42.36111111x. Take half its coefficient (-21.18055556). Square it (448.6159338) and add it to both sides. Add '448.6159338' to each side of the equation. -42.36111111x + 448.6159338 + x2 = -94.44444444 + 448.6159338 Reorder the terms: 448.6159338 + -42.36111111x + x2 = -94.44444444 + 448.6159338 Combine like terms: -94.44444444 + 448.6159338 = 354.17148936 448.6159338 + -42.36111111x + x2 = 354.17148936 Factor a perfect square on the left side: (x + -21.18055556)(x + -21.18055556) = 354.17148936 Calculate the square root of the right side: 18.819444449 Break this problem into two subproblems by setting (x + -21.18055556) equal to 18.819444449 and -18.819444449.Subproblem 1
x + -21.18055556 = 18.819444449 Simplifying x + -21.18055556 = 18.819444449 Reorder the terms: -21.18055556 + x = 18.819444449 Solving -21.18055556 + x = 18.819444449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21.18055556' to each side of the equation. -21.18055556 + 21.18055556 + x = 18.819444449 + 21.18055556 Combine like terms: -21.18055556 + 21.18055556 = 0.00000000 0.00000000 + x = 18.819444449 + 21.18055556 x = 18.819444449 + 21.18055556 Combine like terms: 18.819444449 + 21.18055556 = 40.000000009 x = 40.000000009 Simplifying x = 40.000000009Subproblem 2
x + -21.18055556 = -18.819444449 Simplifying x + -21.18055556 = -18.819444449 Reorder the terms: -21.18055556 + x = -18.819444449 Solving -21.18055556 + x = -18.819444449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21.18055556' to each side of the equation. -21.18055556 + 21.18055556 + x = -18.819444449 + 21.18055556 Combine like terms: -21.18055556 + 21.18055556 = 0.00000000 0.00000000 + x = -18.819444449 + 21.18055556 x = -18.819444449 + 21.18055556 Combine like terms: -18.819444449 + 21.18055556 = 2.361111111 x = 2.361111111 Simplifying x = 2.361111111Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.000000009, 2.361111111}
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