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Simplifying 2x2 = 19x + 24 Reorder the terms: 2x2 = 24 + 19x Solving 2x2 = 24 + 19x Solving for variable 'x'. Reorder the terms: -24 + -19x + 2x2 = 24 + 19x + -24 + -19x Reorder the terms: -24 + -19x + 2x2 = 24 + -24 + 19x + -19x Combine like terms: 24 + -24 = 0 -24 + -19x + 2x2 = 0 + 19x + -19x -24 + -19x + 2x2 = 19x + -19x Combine like terms: 19x + -19x = 0 -24 + -19x + 2x2 = 0 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 = 10.628988008 x = 10.628988008 Simplifying x = 10.628988008Subproblem 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 = -1.128988008 x = -1.128988008 Simplifying x = -1.128988008Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.628988008, -1.128988008}
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