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Simplifying 9x2 + -18x + 9 = 20 Reorder the terms: 9 + -18x + 9x2 = 20 Solving 9 + -18x + 9x2 = 20 Solving for variable 'x'. Reorder the terms: 9 + -20 + -18x + 9x2 = 20 + -20 Combine like terms: 9 + -20 = -11 -11 + -18x + 9x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -11 + -18x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.222222222 + -2x + x2 = 0 Move the constant term to the right: Add '1.222222222' to each side of the equation. -1.222222222 + -2x + 1.222222222 + x2 = 0 + 1.222222222 Reorder the terms: -1.222222222 + 1.222222222 + -2x + x2 = 0 + 1.222222222 Combine like terms: -1.222222222 + 1.222222222 = 0.000000000 0.000000000 + -2x + x2 = 0 + 1.222222222 -2x + x2 = 0 + 1.222222222 Combine like terms: 0 + 1.222222222 = 1.222222222 -2x + x2 = 1.222222222 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 1.222222222 + 1 Reorder the terms: 1 + -2x + x2 = 1.222222222 + 1 Combine like terms: 1.222222222 + 1 = 2.222222222 1 + -2x + x2 = 2.222222222 Factor a perfect square on the left side: (x + -1)(x + -1) = 2.222222222 Calculate the square root of the right side: 1.490711985 Break this problem into two subproblems by setting (x + -1) equal to 1.490711985 and -1.490711985.Subproblem 1
x + -1 = 1.490711985 Simplifying x + -1 = 1.490711985 Reorder the terms: -1 + x = 1.490711985 Solving -1 + x = 1.490711985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.490711985 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.490711985 + 1 x = 1.490711985 + 1 Combine like terms: 1.490711985 + 1 = 2.490711985 x = 2.490711985 Simplifying x = 2.490711985Subproblem 2
x + -1 = -1.490711985 Simplifying x + -1 = -1.490711985 Reorder the terms: -1 + x = -1.490711985 Solving -1 + x = -1.490711985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.490711985 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.490711985 + 1 x = -1.490711985 + 1 Combine like terms: -1.490711985 + 1 = -0.490711985 x = -0.490711985 Simplifying x = -0.490711985Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.490711985, -0.490711985}
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