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Simplifying -3x2 + 9x = 2 Reorder the terms: 9x + -3x2 = 2 Solving 9x + -3x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + 9x + -3x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 9x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 0.6666666667 + -3x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -3x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -3x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -3x + x2 = 0 + -0.6666666667 -3x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -3x + x2 = -0.6666666667 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 = -0.6666666667 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -0.6666666667 + 2.25 Combine like terms: -0.6666666667 + 2.25 = 1.5833333333 2.25 + -3x + x2 = 1.5833333333 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 1.5833333333 Calculate the square root of the right side: 1.258305739 Break this problem into two subproblems by setting (x + -1.5) equal to 1.258305739 and -1.258305739.Subproblem 1
x + -1.5 = 1.258305739 Simplifying x + -1.5 = 1.258305739 Reorder the terms: -1.5 + x = 1.258305739 Solving -1.5 + x = 1.258305739 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 = 1.258305739 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.258305739 + 1.5 x = 1.258305739 + 1.5 Combine like terms: 1.258305739 + 1.5 = 2.758305739 x = 2.758305739 Simplifying x = 2.758305739Subproblem 2
x + -1.5 = -1.258305739 Simplifying x + -1.5 = -1.258305739 Reorder the terms: -1.5 + x = -1.258305739 Solving -1.5 + x = -1.258305739 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 = -1.258305739 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.258305739 + 1.5 x = -1.258305739 + 1.5 Combine like terms: -1.258305739 + 1.5 = 0.241694261 x = 0.241694261 Simplifying x = 0.241694261Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.758305739, 0.241694261}
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