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Simplifying 5x2 + 48x + -720 = 0 Reorder the terms: -720 + 48x + 5x2 = 0 Solving -720 + 48x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -144 + 9.6x + x2 = 0 Move the constant term to the right: Add '144' to each side of the equation. -144 + 9.6x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + 9.6x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 9.6x + x2 = 0 + 144 9.6x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 9.6x + x2 = 144 The x term is 9.6x. Take half its coefficient (4.8). Square it (23.04) and add it to both sides. Add '23.04' to each side of the equation. 9.6x + 23.04 + x2 = 144 + 23.04 Reorder the terms: 23.04 + 9.6x + x2 = 144 + 23.04 Combine like terms: 144 + 23.04 = 167.04 23.04 + 9.6x + x2 = 167.04 Factor a perfect square on the left side: (x + 4.8)(x + 4.8) = 167.04 Calculate the square root of the right side: 12.924395537 Break this problem into two subproblems by setting (x + 4.8) equal to 12.924395537 and -12.924395537.Subproblem 1
x + 4.8 = 12.924395537 Simplifying x + 4.8 = 12.924395537 Reorder the terms: 4.8 + x = 12.924395537 Solving 4.8 + x = 12.924395537 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.8' to each side of the equation. 4.8 + -4.8 + x = 12.924395537 + -4.8 Combine like terms: 4.8 + -4.8 = 0.0 0.0 + x = 12.924395537 + -4.8 x = 12.924395537 + -4.8 Combine like terms: 12.924395537 + -4.8 = 8.124395537 x = 8.124395537 Simplifying x = 8.124395537Subproblem 2
x + 4.8 = -12.924395537 Simplifying x + 4.8 = -12.924395537 Reorder the terms: 4.8 + x = -12.924395537 Solving 4.8 + x = -12.924395537 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.8' to each side of the equation. 4.8 + -4.8 + x = -12.924395537 + -4.8 Combine like terms: 4.8 + -4.8 = 0.0 0.0 + x = -12.924395537 + -4.8 x = -12.924395537 + -4.8 Combine like terms: -12.924395537 + -4.8 = -17.724395537 x = -17.724395537 Simplifying x = -17.724395537Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.124395537, -17.724395537}
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