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Simplifying 2x2 + 9x + 12 = 48 Reorder the terms: 12 + 9x + 2x2 = 48 Solving 12 + 9x + 2x2 = 48 Solving for variable 'x'. Reorder the terms: 12 + -48 + 9x + 2x2 = 48 + -48 Combine like terms: 12 + -48 = -36 -36 + 9x + 2x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -36 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -18 + 4.5x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + 4.5x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 4.5x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 4.5x + x2 = 0 + 18 4.5x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 4.5x + x2 = 18 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 18 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 18 + 5.0625 Combine like terms: 18 + 5.0625 = 23.0625 5.0625 + 4.5x + x2 = 23.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 23.0625 Calculate the square root of the right side: 4.802343178 Break this problem into two subproblems by setting (x + 2.25) equal to 4.802343178 and -4.802343178.Subproblem 1
x + 2.25 = 4.802343178 Simplifying x + 2.25 = 4.802343178 Reorder the terms: 2.25 + x = 4.802343178 Solving 2.25 + x = 4.802343178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 4.802343178 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 4.802343178 + -2.25 x = 4.802343178 + -2.25 Combine like terms: 4.802343178 + -2.25 = 2.552343178 x = 2.552343178 Simplifying x = 2.552343178Subproblem 2
x + 2.25 = -4.802343178 Simplifying x + 2.25 = -4.802343178 Reorder the terms: 2.25 + x = -4.802343178 Solving 2.25 + x = -4.802343178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -4.802343178 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -4.802343178 + -2.25 x = -4.802343178 + -2.25 Combine like terms: -4.802343178 + -2.25 = -7.052343178 x = -7.052343178 Simplifying x = -7.052343178Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.552343178, -7.052343178}
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