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Simplifying -3x2 + -3x + 6 = -4 Reorder the terms: 6 + -3x + -3x2 = -4 Solving 6 + -3x + -3x2 = -4 Solving for variable 'x'. Reorder the terms: 6 + 4 + -3x + -3x2 = -4 + 4 Combine like terms: 6 + 4 = 10 10 + -3x + -3x2 = -4 + 4 Combine like terms: -4 + 4 = 0 10 + -3x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -3.333333333 + x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + x + x2 = 0 + 3.333333333 x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 x + x2 = 3.333333333 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. + 0.25 + x2 = 3.333333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 3.333333333 + 0.25 Combine like terms: 3.333333333 + 0.25 = 3.583333333 1.25 + x2 = 3.583333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3.583333333 Calculate the square root of the right side: 1.892969449 Break this problem into two subproblems by setting (x + 0.5) equal to 1.892969449 and -1.892969449.Subproblem 1
x + 0.5 = 1.892969449 Simplifying x + 0.5 = 1.892969449 Reorder the terms: 0.5 + x = 1.892969449 Solving 0.5 + x = 1.892969449 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 = 1.892969449 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.892969449 + -0.5 x = 1.892969449 + -0.5 Combine like terms: 1.892969449 + -0.5 = 1.392969449 x = 1.392969449 Simplifying x = 1.392969449Subproblem 2
x + 0.5 = -1.892969449 Simplifying x + 0.5 = -1.892969449 Reorder the terms: 0.5 + x = -1.892969449 Solving 0.5 + x = -1.892969449 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 = -1.892969449 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.892969449 + -0.5 x = -1.892969449 + -0.5 Combine like terms: -1.892969449 + -0.5 = -2.392969449 x = -2.392969449 Simplifying x = -2.392969449Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.392969449, -2.392969449}
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