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Simplifying 3x2 + 3x + -65 = 0 Reorder the terms: -65 + 3x + 3x2 = 0 Solving -65 + 3x + 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'. -21.66666667 + x + x2 = 0 Move the constant term to the right: Add '21.66666667' to each side of the equation. -21.66666667 + x + 21.66666667 + x2 = 0 + 21.66666667 Reorder the terms: -21.66666667 + 21.66666667 + x + x2 = 0 + 21.66666667 Combine like terms: -21.66666667 + 21.66666667 = 0.00000000 0.00000000 + x + x2 = 0 + 21.66666667 x + x2 = 0 + 21.66666667 Combine like terms: 0 + 21.66666667 = 21.66666667 x + x2 = 21.66666667 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 = 21.66666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 21.66666667 + 0.25 Combine like terms: 21.66666667 + 0.25 = 21.91666667 1.25 + x2 = 21.91666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 21.91666667 Calculate the square root of the right side: 4.681523969 Break this problem into two subproblems by setting (x + 0.5) equal to 4.681523969 and -4.681523969.Subproblem 1
x + 0.5 = 4.681523969 Simplifying x + 0.5 = 4.681523969 Reorder the terms: 0.5 + x = 4.681523969 Solving 0.5 + x = 4.681523969 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 = 4.681523969 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.681523969 + -0.5 x = 4.681523969 + -0.5 Combine like terms: 4.681523969 + -0.5 = 4.181523969 x = 4.181523969 Simplifying x = 4.181523969Subproblem 2
x + 0.5 = -4.681523969 Simplifying x + 0.5 = -4.681523969 Reorder the terms: 0.5 + x = -4.681523969 Solving 0.5 + x = -4.681523969 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 = -4.681523969 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.681523969 + -0.5 x = -4.681523969 + -0.5 Combine like terms: -4.681523969 + -0.5 = -5.181523969 x = -5.181523969 Simplifying x = -5.181523969Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.181523969, -5.181523969}
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