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Simplifying 0 = -2x2 + -13x + 48 Reorder the terms: 0 = 48 + -13x + -2x2 Solving 0 = 48 + -13x + -2x2 Solving for variable 'x'. Combine like terms: 0 + -48 = -48 -48 + 13x + 2x2 = 48 + -13x + -2x2 + -48 + 13x + 2x2 Reorder the terms: -48 + 13x + 2x2 = 48 + -48 + -13x + 13x + -2x2 + 2x2 Combine like terms: 48 + -48 = 0 -48 + 13x + 2x2 = 0 + -13x + 13x + -2x2 + 2x2 -48 + 13x + 2x2 = -13x + 13x + -2x2 + 2x2 Combine like terms: -13x + 13x = 0 -48 + 13x + 2x2 = 0 + -2x2 + 2x2 -48 + 13x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -48 + 13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -24 + 6.5x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 6.5x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 6.5x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 6.5x + x2 = 0 + 24 6.5x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 6.5x + x2 = 24 The x term is 6.5x. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5x + 10.5625 + x2 = 24 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = 24 + 10.5625 Combine like terms: 24 + 10.5625 = 34.5625 10.5625 + 6.5x + x2 = 34.5625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 34.5625 Calculate the square root of the right side: 5.878988008 Break this problem into two subproblems by setting (x + 3.25) equal to 5.878988008 and -5.878988008.Subproblem 1
x + 3.25 = 5.878988008 Simplifying x + 3.25 = 5.878988008 Reorder the terms: 3.25 + x = 5.878988008 Solving 3.25 + x = 5.878988008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 5.878988008 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 5.878988008 + -3.25 x = 5.878988008 + -3.25 Combine like terms: 5.878988008 + -3.25 = 2.628988008 x = 2.628988008 Simplifying x = 2.628988008Subproblem 2
x + 3.25 = -5.878988008 Simplifying x + 3.25 = -5.878988008 Reorder the terms: 3.25 + x = -5.878988008 Solving 3.25 + x = -5.878988008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -5.878988008 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -5.878988008 + -3.25 x = -5.878988008 + -3.25 Combine like terms: -5.878988008 + -3.25 = -9.128988008 x = -9.128988008 Simplifying x = -9.128988008Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.628988008, -9.128988008}
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