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Simplifying 3x * x + 3x = 80 Multiply x * x 3x2 + 3x = 80 Reorder the terms: 3x + 3x2 = 80 Solving 3x + 3x2 = 80 Solving for variable 'x'. Reorder the terms: -80 + 3x + 3x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + 3x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -26.66666667 + x + x2 = 0 Move the constant term to the right: Add '26.66666667' to each side of the equation. -26.66666667 + x + 26.66666667 + x2 = 0 + 26.66666667 Reorder the terms: -26.66666667 + 26.66666667 + x + x2 = 0 + 26.66666667 Combine like terms: -26.66666667 + 26.66666667 = 0.00000000 0.00000000 + x + x2 = 0 + 26.66666667 x + x2 = 0 + 26.66666667 Combine like terms: 0 + 26.66666667 = 26.66666667 x + x2 = 26.66666667 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 = 26.66666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 26.66666667 + 0.25 Combine like terms: 26.66666667 + 0.25 = 26.91666667 1.25 + x2 = 26.91666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 26.91666667 Calculate the square root of the right side: 5.188127472 Break this problem into two subproblems by setting (x + 0.5) equal to 5.188127472 and -5.188127472.Subproblem 1
x + 0.5 = 5.188127472 Simplifying x + 0.5 = 5.188127472 Reorder the terms: 0.5 + x = 5.188127472 Solving 0.5 + x = 5.188127472 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 = 5.188127472 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.188127472 + -0.5 x = 5.188127472 + -0.5 Combine like terms: 5.188127472 + -0.5 = 4.688127472 x = 4.688127472 Simplifying x = 4.688127472Subproblem 2
x + 0.5 = -5.188127472 Simplifying x + 0.5 = -5.188127472 Reorder the terms: 0.5 + x = -5.188127472 Solving 0.5 + x = -5.188127472 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 = -5.188127472 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.188127472 + -0.5 x = -5.188127472 + -0.5 Combine like terms: -5.188127472 + -0.5 = -5.688127472 x = -5.688127472 Simplifying x = -5.688127472Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.688127472, -5.688127472}
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