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Simplifying 5x2 + -48x + -96 = 0 Reorder the terms: -96 + -48x + 5x2 = 0 Solving -96 + -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'. -19.2 + -9.6x + x2 = 0 Move the constant term to the right: Add '19.2' to each side of the equation. -19.2 + -9.6x + 19.2 + x2 = 0 + 19.2 Reorder the terms: -19.2 + 19.2 + -9.6x + x2 = 0 + 19.2 Combine like terms: -19.2 + 19.2 = 0.0 0.0 + -9.6x + x2 = 0 + 19.2 -9.6x + x2 = 0 + 19.2 Combine like terms: 0 + 19.2 = 19.2 -9.6x + x2 = 19.2 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 = 19.2 + 23.04 Reorder the terms: 23.04 + -9.6x + x2 = 19.2 + 23.04 Combine like terms: 19.2 + 23.04 = 42.24 23.04 + -9.6x + x2 = 42.24 Factor a perfect square on the left side: (x + -4.8)(x + -4.8) = 42.24 Calculate the square root of the right side: 6.499230724 Break this problem into two subproblems by setting (x + -4.8) equal to 6.499230724 and -6.499230724.Subproblem 1
x + -4.8 = 6.499230724 Simplifying x + -4.8 = 6.499230724 Reorder the terms: -4.8 + x = 6.499230724 Solving -4.8 + x = 6.499230724 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 = 6.499230724 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + x = 6.499230724 + 4.8 x = 6.499230724 + 4.8 Combine like terms: 6.499230724 + 4.8 = 11.299230724 x = 11.299230724 Simplifying x = 11.299230724Subproblem 2
x + -4.8 = -6.499230724 Simplifying x + -4.8 = -6.499230724 Reorder the terms: -4.8 + x = -6.499230724 Solving -4.8 + x = -6.499230724 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 = -6.499230724 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + x = -6.499230724 + 4.8 x = -6.499230724 + 4.8 Combine like terms: -6.499230724 + 4.8 = -1.699230724 x = -1.699230724 Simplifying x = -1.699230724Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.299230724, -1.699230724}
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