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Simplifying 2x(2x + 24 + x) = 81 Reorder the terms: 2x(24 + 2x + x) = 81 Combine like terms: 2x + x = 3x 2x(24 + 3x) = 81 (24 * 2x + 3x * 2x) = 81 (48x + 6x2) = 81 Solving 48x + 6x2 = 81 Solving for variable 'x'. Reorder the terms: -81 + 48x + 6x2 = 81 + -81 Combine like terms: 81 + -81 = 0 -81 + 48x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-27 + 16x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-27 + 16x + 2x2)' equal to zero and attempt to solve: Simplifying -27 + 16x + 2x2 = 0 Solving -27 + 16x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -13.5 + 8x + x2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + 8x + 13.5 + x2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + 8x + x2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + 8x + x2 = 0 + 13.5 8x + x2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 8x + x2 = 13.5 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 13.5 + 16 Reorder the terms: 16 + 8x + x2 = 13.5 + 16 Combine like terms: 13.5 + 16 = 29.5 16 + 8x + x2 = 29.5 Factor a perfect square on the left side: (x + 4)(x + 4) = 29.5 Calculate the square root of the right side: 5.431390246 Break this problem into two subproblems by setting (x + 4) equal to 5.431390246 and -5.431390246.Subproblem 1
x + 4 = 5.431390246 Simplifying x + 4 = 5.431390246 Reorder the terms: 4 + x = 5.431390246 Solving 4 + x = 5.431390246 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 5.431390246 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.431390246 + -4 x = 5.431390246 + -4 Combine like terms: 5.431390246 + -4 = 1.431390246 x = 1.431390246 Simplifying x = 1.431390246Subproblem 2
x + 4 = -5.431390246 Simplifying x + 4 = -5.431390246 Reorder the terms: 4 + x = -5.431390246 Solving 4 + x = -5.431390246 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -5.431390246 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.431390246 + -4 x = -5.431390246 + -4 Combine like terms: -5.431390246 + -4 = -9.431390246 x = -9.431390246 Simplifying x = -9.431390246Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.431390246, -9.431390246}Solution
x = {1.431390246, -9.431390246}
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