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Simplifying 2x2 + 6x + 9 = 20 Reorder the terms: 9 + 6x + 2x2 = 20 Solving 9 + 6x + 2x2 = 20 Solving for variable 'x'. Reorder the terms: 9 + -20 + 6x + 2x2 = 20 + -20 Combine like terms: 9 + -20 = -11 -11 + 6x + 2x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -11 + 6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5.5 + 3x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 3x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 3x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 3x + x2 = 0 + 5.5 3x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 3x + x2 = 5.5 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 5.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 5.5 + 2.25 Combine like terms: 5.5 + 2.25 = 7.75 2.25 + 3x + x2 = 7.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 7.75 Calculate the square root of the right side: 2.783882181 Break this problem into two subproblems by setting (x + 1.5) equal to 2.783882181 and -2.783882181.Subproblem 1
x + 1.5 = 2.783882181 Simplifying x + 1.5 = 2.783882181 Reorder the terms: 1.5 + x = 2.783882181 Solving 1.5 + x = 2.783882181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.783882181 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.783882181 + -1.5 x = 2.783882181 + -1.5 Combine like terms: 2.783882181 + -1.5 = 1.283882181 x = 1.283882181 Simplifying x = 1.283882181Subproblem 2
x + 1.5 = -2.783882181 Simplifying x + 1.5 = -2.783882181 Reorder the terms: 1.5 + x = -2.783882181 Solving 1.5 + x = -2.783882181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.783882181 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.783882181 + -1.5 x = -2.783882181 + -1.5 Combine like terms: -2.783882181 + -1.5 = -4.283882181 x = -4.283882181 Simplifying x = -4.283882181Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.283882181, -4.283882181}
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