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Simplifying 5x2 + 25x + -48 = 0 Reorder the terms: -48 + 25x + 5x2 = 0 Solving -48 + 25x + 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'. -9.6 + 5x + x2 = 0 Move the constant term to the right: Add '9.6' to each side of the equation. -9.6 + 5x + 9.6 + x2 = 0 + 9.6 Reorder the terms: -9.6 + 9.6 + 5x + x2 = 0 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + 5x + x2 = 0 + 9.6 5x + x2 = 0 + 9.6 Combine like terms: 0 + 9.6 = 9.6 5x + x2 = 9.6 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 9.6 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 9.6 + 6.25 Combine like terms: 9.6 + 6.25 = 15.85 6.25 + 5x + x2 = 15.85 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 15.85 Calculate the square root of the right side: 3.981205847 Break this problem into two subproblems by setting (x + 2.5) equal to 3.981205847 and -3.981205847.Subproblem 1
x + 2.5 = 3.981205847 Simplifying x + 2.5 = 3.981205847 Reorder the terms: 2.5 + x = 3.981205847 Solving 2.5 + x = 3.981205847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 3.981205847 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.981205847 + -2.5 x = 3.981205847 + -2.5 Combine like terms: 3.981205847 + -2.5 = 1.481205847 x = 1.481205847 Simplifying x = 1.481205847Subproblem 2
x + 2.5 = -3.981205847 Simplifying x + 2.5 = -3.981205847 Reorder the terms: 2.5 + x = -3.981205847 Solving 2.5 + x = -3.981205847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -3.981205847 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.981205847 + -2.5 x = -3.981205847 + -2.5 Combine like terms: -3.981205847 + -2.5 = -6.481205847 x = -6.481205847 Simplifying x = -6.481205847Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.481205847, -6.481205847}
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