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Simplifying -3x2 + -9x + 11 = 0 Reorder the terms: 11 + -9x + -3x2 = 0 Solving 11 + -9x + -3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -3.666666667 + 3x + x2 = 0 Move the constant term to the right: Add '3.666666667' to each side of the equation. -3.666666667 + 3x + 3.666666667 + x2 = 0 + 3.666666667 Reorder the terms: -3.666666667 + 3.666666667 + 3x + x2 = 0 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + 3x + x2 = 0 + 3.666666667 3x + x2 = 0 + 3.666666667 Combine like terms: 0 + 3.666666667 = 3.666666667 3x + x2 = 3.666666667 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 = 3.666666667 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 3.666666667 + 2.25 Combine like terms: 3.666666667 + 2.25 = 5.916666667 2.25 + 3x + x2 = 5.916666667 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 5.916666667 Calculate the square root of the right side: 2.43241992 Break this problem into two subproblems by setting (x + 1.5) equal to 2.43241992 and -2.43241992.Subproblem 1
x + 1.5 = 2.43241992 Simplifying x + 1.5 = 2.43241992 Reorder the terms: 1.5 + x = 2.43241992 Solving 1.5 + x = 2.43241992 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 = 2.43241992 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.43241992 + -1.5 x = 2.43241992 + -1.5 Combine like terms: 2.43241992 + -1.5 = 0.93241992 x = 0.93241992 Simplifying x = 0.93241992Subproblem 2
x + 1.5 = -2.43241992 Simplifying x + 1.5 = -2.43241992 Reorder the terms: 1.5 + x = -2.43241992 Solving 1.5 + x = -2.43241992 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 = -2.43241992 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.43241992 + -1.5 x = -2.43241992 + -1.5 Combine like terms: -2.43241992 + -1.5 = -3.93241992 x = -3.93241992 Simplifying x = -3.93241992Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.93241992, -3.93241992}
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