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Simplifying 3x2 + 6 + x + -3 = 81 Reorder the terms: 6 + -3 + x + 3x2 = 81 Combine like terms: 6 + -3 = 3 3 + x + 3x2 = 81 Solving 3 + x + 3x2 = 81 Solving for variable 'x'. Reorder the terms: 3 + -81 + x + 3x2 = 81 + -81 Combine like terms: 3 + -81 = -78 -78 + x + 3x2 = 81 + -81 Combine like terms: 81 + -81 = 0 -78 + x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -26 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '26' to each side of the equation. -26 + 0.3333333333x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + 0.3333333333x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 0.3333333333x + x2 = 0 + 26 0.3333333333x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 0.3333333333x + x2 = 26 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. 0.3333333333x + 0.25 + x2 = 26 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = 26 + 0.25 Combine like terms: 26 + 0.25 = 26.25 0.25 + 0.3333333333x + x2 = 26.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (x + 0.5) equal to 5.123475383 and -5.123475383.Subproblem 1
x + 0.5 = 5.123475383 Simplifying x + 0.5 = 5.123475383 Reorder the terms: 0.5 + x = 5.123475383 Solving 0.5 + x = 5.123475383 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 = 5.123475383 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.123475383 + -0.5 x = 5.123475383 + -0.5 Combine like terms: 5.123475383 + -0.5 = 4.623475383 x = 4.623475383 Simplifying x = 4.623475383Subproblem 2
x + 0.5 = -5.123475383 Simplifying x + 0.5 = -5.123475383 Reorder the terms: 0.5 + x = -5.123475383 Solving 0.5 + x = -5.123475383 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 = -5.123475383 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.123475383 + -0.5 x = -5.123475383 + -0.5 Combine like terms: -5.123475383 + -0.5 = -5.623475383 x = -5.623475383 Simplifying x = -5.623475383Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.623475383, -5.623475383}
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