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Simplifying 9x2 + x + -28 = 0 Reorder the terms: -28 + x + 9x2 = 0 Solving -28 + x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -3.111111111 + 0.1111111111x + x2 = 0 Move the constant term to the right: Add '3.111111111' to each side of the equation. -3.111111111 + 0.1111111111x + 3.111111111 + x2 = 0 + 3.111111111 Reorder the terms: -3.111111111 + 3.111111111 + 0.1111111111x + x2 = 0 + 3.111111111 Combine like terms: -3.111111111 + 3.111111111 = 0.000000000 0.000000000 + 0.1111111111x + x2 = 0 + 3.111111111 0.1111111111x + x2 = 0 + 3.111111111 Combine like terms: 0 + 3.111111111 = 3.111111111 0.1111111111x + x2 = 3.111111111 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. 0.1111111111x + 0.25 + x2 = 3.111111111 + 0.25 Reorder the terms: 0.25 + 0.1111111111x + x2 = 3.111111111 + 0.25 Combine like terms: 3.111111111 + 0.25 = 3.361111111 0.25 + 0.1111111111x + x2 = 3.361111111 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3.361111111 Calculate the square root of the right side: 1.833333333 Break this problem into two subproblems by setting (x + 0.5) equal to 1.833333333 and -1.833333333.Subproblem 1
x + 0.5 = 1.833333333 Simplifying x + 0.5 = 1.833333333 Reorder the terms: 0.5 + x = 1.833333333 Solving 0.5 + x = 1.833333333 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 = 1.833333333 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.833333333 + -0.5 x = 1.833333333 + -0.5 Combine like terms: 1.833333333 + -0.5 = 1.333333333 x = 1.333333333 Simplifying x = 1.333333333Subproblem 2
x + 0.5 = -1.833333333 Simplifying x + 0.5 = -1.833333333 Reorder the terms: 0.5 + x = -1.833333333 Solving 0.5 + x = -1.833333333 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 = -1.833333333 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.833333333 + -0.5 x = -1.833333333 + -0.5 Combine like terms: -1.833333333 + -0.5 = -2.333333333 x = -2.333333333 Simplifying x = -2.333333333Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.333333333, -2.333333333}
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