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Simplifying 0 = 3x2 + -9x + -4 Reorder the terms: 0 = -4 + -9x + 3x2 Solving 0 = -4 + -9x + 3x2 Solving for variable 'x'. Combine like terms: 0 + 4 = 4 4 + 9x + -3x2 = -4 + -9x + 3x2 + 4 + 9x + -3x2 Reorder the terms: 4 + 9x + -3x2 = -4 + 4 + -9x + 9x + 3x2 + -3x2 Combine like terms: -4 + 4 = 0 4 + 9x + -3x2 = 0 + -9x + 9x + 3x2 + -3x2 4 + 9x + -3x2 = -9x + 9x + 3x2 + -3x2 Combine like terms: -9x + 9x = 0 4 + 9x + -3x2 = 0 + 3x2 + -3x2 4 + 9x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 4 + 9x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -1.333333333 + -3x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -3x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -3x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -3x + x2 = 0 + 1.333333333 -3x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -3x + x2 = 1.333333333 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 = 1.333333333 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 1.333333333 + 2.25 Combine like terms: 1.333333333 + 2.25 = 3.583333333 2.25 + -3x + x2 = 3.583333333 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 3.583333333 Calculate the square root of the right side: 1.892969449 Break this problem into two subproblems by setting (x + -1.5) equal to 1.892969449 and -1.892969449.Subproblem 1
x + -1.5 = 1.892969449 Simplifying x + -1.5 = 1.892969449 Reorder the terms: -1.5 + x = 1.892969449 Solving -1.5 + x = 1.892969449 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 = 1.892969449 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.892969449 + 1.5 x = 1.892969449 + 1.5 Combine like terms: 1.892969449 + 1.5 = 3.392969449 x = 3.392969449 Simplifying x = 3.392969449Subproblem 2
x + -1.5 = -1.892969449 Simplifying x + -1.5 = -1.892969449 Reorder the terms: -1.5 + x = -1.892969449 Solving -1.5 + x = -1.892969449 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 = -1.892969449 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.892969449 + 1.5 x = -1.892969449 + 1.5 Combine like terms: -1.892969449 + 1.5 = -0.392969449 x = -0.392969449 Simplifying x = -0.392969449Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.392969449, -0.392969449}
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