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Simplifying 2x2 + -9x = 48 Reorder the terms: -9x + 2x2 = 48 Solving -9x + 2x2 = 48 Solving for variable 'x'. Reorder the terms: -48 + -9x + 2x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -48 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -24 + -4.5x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + -4.5x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -4.5x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -4.5x + x2 = 0 + 24 -4.5x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -4.5x + x2 = 24 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 = 24 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 24 + 5.0625 Combine like terms: 24 + 5.0625 = 29.0625 5.0625 + -4.5x + x2 = 29.0625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 29.0625 Calculate the square root of the right side: 5.390964663 Break this problem into two subproblems by setting (x + -2.25) equal to 5.390964663 and -5.390964663.Subproblem 1
x + -2.25 = 5.390964663 Simplifying x + -2.25 = 5.390964663 Reorder the terms: -2.25 + x = 5.390964663 Solving -2.25 + x = 5.390964663 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 = 5.390964663 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 5.390964663 + 2.25 x = 5.390964663 + 2.25 Combine like terms: 5.390964663 + 2.25 = 7.640964663 x = 7.640964663 Simplifying x = 7.640964663Subproblem 2
x + -2.25 = -5.390964663 Simplifying x + -2.25 = -5.390964663 Reorder the terms: -2.25 + x = -5.390964663 Solving -2.25 + x = -5.390964663 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 = -5.390964663 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -5.390964663 + 2.25 x = -5.390964663 + 2.25 Combine like terms: -5.390964663 + 2.25 = -3.140964663 x = -3.140964663 Simplifying x = -3.140964663Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.640964663, -3.140964663}
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