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Simplifying -24 + 19x + 2x2 = 0 Solving -24 + 19x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12 + 9.5x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 9.5x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 9.5x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 9.5x + x2 = 0 + 12 9.5x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 9.5x + x2 = 12 The x term is 9.5x. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5x + 22.5625 + x2 = 12 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = 12 + 22.5625 Combine like terms: 12 + 22.5625 = 34.5625 22.5625 + 9.5x + x2 = 34.5625 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 34.5625 Calculate the square root of the right side: 5.878988008 Break this problem into two subproblems by setting (x + 4.75) equal to 5.878988008 and -5.878988008.Subproblem 1
x + 4.75 = 5.878988008 Simplifying x + 4.75 = 5.878988008 Reorder the terms: 4.75 + x = 5.878988008 Solving 4.75 + x = 5.878988008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = 5.878988008 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 5.878988008 + -4.75 x = 5.878988008 + -4.75 Combine like terms: 5.878988008 + -4.75 = 1.128988008 x = 1.128988008 Simplifying x = 1.128988008Subproblem 2
x + 4.75 = -5.878988008 Simplifying x + 4.75 = -5.878988008 Reorder the terms: 4.75 + x = -5.878988008 Solving 4.75 + x = -5.878988008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = -5.878988008 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -5.878988008 + -4.75 x = -5.878988008 + -4.75 Combine like terms: -5.878988008 + -4.75 = -10.628988008 x = -10.628988008 Simplifying x = -10.628988008Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.128988008, -10.628988008}
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