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Simplifying x2 + x2 + 9x = 20.25 Reorder the terms: 9x + x2 + x2 = 20.25 Combine like terms: x2 + x2 = 2x2 9x + 2x2 = 20.25 Solving 9x + 2x2 = 20.25 Solving for variable 'x'. Reorder the terms: -20.25 + 9x + 2x2 = 20.25 + -20.25 Combine like terms: 20.25 + -20.25 = 0.00 -20.25 + 9x + 2x2 = 0.00 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10.125 + 4.5x + x2 = 0.00 Move the constant term to the right: Add '10.125' to each side of the equation. -10.125 + 4.5x + 10.125 + x2 = 0.00 + 10.125 Reorder the terms: -10.125 + 10.125 + 4.5x + x2 = 0.00 + 10.125 Combine like terms: -10.125 + 10.125 = 0.000 0.000 + 4.5x + x2 = 0.00 + 10.125 4.5x + x2 = 0.00 + 10.125 Combine like terms: 0.00 + 10.125 = 10.125 4.5x + x2 = 10.125 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 = 10.125 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 10.125 + 5.0625 Combine like terms: 10.125 + 5.0625 = 15.1875 5.0625 + 4.5x + x2 = 15.1875 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 15.1875 Calculate the square root of the right side: 3.897114317 Break this problem into two subproblems by setting (x + 2.25) equal to 3.897114317 and -3.897114317.Subproblem 1
x + 2.25 = 3.897114317 Simplifying x + 2.25 = 3.897114317 Reorder the terms: 2.25 + x = 3.897114317 Solving 2.25 + x = 3.897114317 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 = 3.897114317 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 3.897114317 + -2.25 x = 3.897114317 + -2.25 Combine like terms: 3.897114317 + -2.25 = 1.647114317 x = 1.647114317 Simplifying x = 1.647114317Subproblem 2
x + 2.25 = -3.897114317 Simplifying x + 2.25 = -3.897114317 Reorder the terms: 2.25 + x = -3.897114317 Solving 2.25 + x = -3.897114317 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 = -3.897114317 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -3.897114317 + -2.25 x = -3.897114317 + -2.25 Combine like terms: -3.897114317 + -2.25 = -6.147114317 x = -6.147114317 Simplifying x = -6.147114317Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.647114317, -6.147114317}
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