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Simplifying 9x2 + 9x = 20 Reorder the terms: 9x + 9x2 = 20 Solving 9x + 9x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + 9x + 9x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 9x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.222222222 + x + x2 = 0 Move the constant term to the right: Add '2.222222222' to each side of the equation. -2.222222222 + x + 2.222222222 + x2 = 0 + 2.222222222 Reorder the terms: -2.222222222 + 2.222222222 + x + x2 = 0 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + x + x2 = 0 + 2.222222222 x + x2 = 0 + 2.222222222 Combine like terms: 0 + 2.222222222 = 2.222222222 x + x2 = 2.222222222 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 2.222222222 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 2.222222222 + 0.25 Combine like terms: 2.222222222 + 0.25 = 2.472222222 1.25 + x2 = 2.472222222 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.472222222 Calculate the square root of the right side: 1.572330189 Break this problem into two subproblems by setting (x + 0.5) equal to 1.572330189 and -1.572330189.Subproblem 1
x + 0.5 = 1.572330189 Simplifying x + 0.5 = 1.572330189 Reorder the terms: 0.5 + x = 1.572330189 Solving 0.5 + x = 1.572330189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.572330189 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.572330189 + -0.5 x = 1.572330189 + -0.5 Combine like terms: 1.572330189 + -0.5 = 1.072330189 x = 1.072330189 Simplifying x = 1.072330189Subproblem 2
x + 0.5 = -1.572330189 Simplifying x + 0.5 = -1.572330189 Reorder the terms: 0.5 + x = -1.572330189 Solving 0.5 + x = -1.572330189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.572330189 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.572330189 + -0.5 x = -1.572330189 + -0.5 Combine like terms: -1.572330189 + -0.5 = -2.072330189 x = -2.072330189 Simplifying x = -2.072330189Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.072330189, -2.072330189}
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