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Simplifying 33x(x + 4) = 8320 Reorder the terms: 33x(4 + x) = 8320 (4 * 33x + x * 33x) = 8320 (132x + 33x2) = 8320 Solving 132x + 33x2 = 8320 Solving for variable 'x'. Reorder the terms: -8320 + 132x + 33x2 = 8320 + -8320 Combine like terms: 8320 + -8320 = 0 -8320 + 132x + 33x2 = 0 Begin completing the square. Divide all terms by 33 the coefficient of the squared term: Divide each side by '33'. -252.1212121 + 4x + x2 = 0 Move the constant term to the right: Add '252.1212121' to each side of the equation. -252.1212121 + 4x + 252.1212121 + x2 = 0 + 252.1212121 Reorder the terms: -252.1212121 + 252.1212121 + 4x + x2 = 0 + 252.1212121 Combine like terms: -252.1212121 + 252.1212121 = 0.0000000 0.0000000 + 4x + x2 = 0 + 252.1212121 4x + x2 = 0 + 252.1212121 Combine like terms: 0 + 252.1212121 = 252.1212121 4x + x2 = 252.1212121 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 252.1212121 + 4 Reorder the terms: 4 + 4x + x2 = 252.1212121 + 4 Combine like terms: 252.1212121 + 4 = 256.1212121 4 + 4x + x2 = 256.1212121 Factor a perfect square on the left side: (x + 2)(x + 2) = 256.1212121 Calculate the square root of the right side: 16.00378743 Break this problem into two subproblems by setting (x + 2) equal to 16.00378743 and -16.00378743.Subproblem 1
x + 2 = 16.00378743 Simplifying x + 2 = 16.00378743 Reorder the terms: 2 + x = 16.00378743 Solving 2 + x = 16.00378743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 16.00378743 + -2 Combine like terms: 2 + -2 = 0 0 + x = 16.00378743 + -2 x = 16.00378743 + -2 Combine like terms: 16.00378743 + -2 = 14.00378743 x = 14.00378743 Simplifying x = 14.00378743Subproblem 2
x + 2 = -16.00378743 Simplifying x + 2 = -16.00378743 Reorder the terms: 2 + x = -16.00378743 Solving 2 + x = -16.00378743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -16.00378743 + -2 Combine like terms: 2 + -2 = 0 0 + x = -16.00378743 + -2 x = -16.00378743 + -2 Combine like terms: -16.00378743 + -2 = -18.00378743 x = -18.00378743 Simplifying x = -18.00378743Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.00378743, -18.00378743}
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