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Simplifying 0.2x2 + 24x + -720 = 0 Reorder the terms: -720 + 24x + 0.2x2 = 0 Solving -720 + 24x + 0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -3600 + 120x + x2 = 0 Move the constant term to the right: Add '3600' to each side of the equation. -3600 + 120x + 3600 + x2 = 0 + 3600 Reorder the terms: -3600 + 3600 + 120x + x2 = 0 + 3600 Combine like terms: -3600 + 3600 = 0 0 + 120x + x2 = 0 + 3600 120x + x2 = 0 + 3600 Combine like terms: 0 + 3600 = 3600 120x + x2 = 3600 The x term is 120x. Take half its coefficient (60). Square it (3600) and add it to both sides. Add '3600' to each side of the equation. 120x + 3600 + x2 = 3600 + 3600 Reorder the terms: 3600 + 120x + x2 = 3600 + 3600 Combine like terms: 3600 + 3600 = 7200 3600 + 120x + x2 = 7200 Factor a perfect square on the left side: (x + 60)(x + 60) = 7200 Calculate the square root of the right side: 84.852813742 Break this problem into two subproblems by setting (x + 60) equal to 84.852813742 and -84.852813742.Subproblem 1
x + 60 = 84.852813742 Simplifying x + 60 = 84.852813742 Reorder the terms: 60 + x = 84.852813742 Solving 60 + x = 84.852813742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-60' to each side of the equation. 60 + -60 + x = 84.852813742 + -60 Combine like terms: 60 + -60 = 0 0 + x = 84.852813742 + -60 x = 84.852813742 + -60 Combine like terms: 84.852813742 + -60 = 24.852813742 x = 24.852813742 Simplifying x = 24.852813742Subproblem 2
x + 60 = -84.852813742 Simplifying x + 60 = -84.852813742 Reorder the terms: 60 + x = -84.852813742 Solving 60 + x = -84.852813742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-60' to each side of the equation. 60 + -60 + x = -84.852813742 + -60 Combine like terms: 60 + -60 = 0 0 + x = -84.852813742 + -60 x = -84.852813742 + -60 Combine like terms: -84.852813742 + -60 = -144.852813742 x = -144.852813742 Simplifying x = -144.852813742Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.852813742, -144.852813742}
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