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Simplifying 3x2 + -9x + 20.25 = 21.25 Reorder the terms: 20.25 + -9x + 3x2 = 21.25 Solving 20.25 + -9x + 3x2 = 21.25 Solving for variable 'x'. Reorder the terms: 20.25 + -21.25 + -9x + 3x2 = 21.25 + -21.25 Combine like terms: 20.25 + -21.25 = -1 -1 + -9x + 3x2 = 21.25 + -21.25 Combine like terms: 21.25 + -21.25 = 0.00 -1 + -9x + 3x2 = 0.00 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.3333333333 + -3x + x2 = 0.00 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -3x + 0.3333333333 + x2 = 0.00 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -3x + x2 = 0.00 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -3x + x2 = 0.00 + 0.3333333333 -3x + x2 = 0.00 + 0.3333333333 Combine like terms: 0.00 + 0.3333333333 = 0.3333333333 -3x + x2 = 0.3333333333 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 = 0.3333333333 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 0.3333333333 + 2.25 Combine like terms: 0.3333333333 + 2.25 = 2.5833333333 2.25 + -3x + x2 = 2.5833333333 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 2.5833333333 Calculate the square root of the right side: 1.607275127 Break this problem into two subproblems by setting (x + -1.5) equal to 1.607275127 and -1.607275127.Subproblem 1
x + -1.5 = 1.607275127 Simplifying x + -1.5 = 1.607275127 Reorder the terms: -1.5 + x = 1.607275127 Solving -1.5 + x = 1.607275127 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 = 1.607275127 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.607275127 + 1.5 x = 1.607275127 + 1.5 Combine like terms: 1.607275127 + 1.5 = 3.107275127 x = 3.107275127 Simplifying x = 3.107275127Subproblem 2
x + -1.5 = -1.607275127 Simplifying x + -1.5 = -1.607275127 Reorder the terms: -1.5 + x = -1.607275127 Solving -1.5 + x = -1.607275127 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 = -1.607275127 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.607275127 + 1.5 x = -1.607275127 + 1.5 Combine like terms: -1.607275127 + 1.5 = -0.107275127 x = -0.107275127 Simplifying x = -0.107275127Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.107275127, -0.107275127}
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