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Simplifying x(x + 4) = 32.64 Reorder the terms: x(4 + x) = 32.64 (4 * x + x * x) = 32.64 (4x + x2) = 32.64 Solving 4x + x2 = 32.64 Solving for variable 'x'. Reorder the terms: -32.64 + 4x + x2 = 32.64 + -32.64 Combine like terms: 32.64 + -32.64 = 0.00 -32.64 + 4x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '32.64' to each side of the equation. -32.64 + 4x + 32.64 + x2 = 0.00 + 32.64 Reorder the terms: -32.64 + 32.64 + 4x + x2 = 0.00 + 32.64 Combine like terms: -32.64 + 32.64 = 0.00 0.00 + 4x + x2 = 0.00 + 32.64 4x + x2 = 0.00 + 32.64 Combine like terms: 0.00 + 32.64 = 32.64 4x + x2 = 32.64 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 = 32.64 + 4 Reorder the terms: 4 + 4x + x2 = 32.64 + 4 Combine like terms: 32.64 + 4 = 36.64 4 + 4x + x2 = 36.64 Factor a perfect square on the left side: (x + 2)(x + 2) = 36.64 Calculate the square root of the right side: 6.05309838 Break this problem into two subproblems by setting (x + 2) equal to 6.05309838 and -6.05309838.Subproblem 1
x + 2 = 6.05309838 Simplifying x + 2 = 6.05309838 Reorder the terms: 2 + x = 6.05309838 Solving 2 + x = 6.05309838 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 = 6.05309838 + -2 Combine like terms: 2 + -2 = 0 0 + x = 6.05309838 + -2 x = 6.05309838 + -2 Combine like terms: 6.05309838 + -2 = 4.05309838 x = 4.05309838 Simplifying x = 4.05309838Subproblem 2
x + 2 = -6.05309838 Simplifying x + 2 = -6.05309838 Reorder the terms: 2 + x = -6.05309838 Solving 2 + x = -6.05309838 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 = -6.05309838 + -2 Combine like terms: 2 + -2 = 0 0 + x = -6.05309838 + -2 x = -6.05309838 + -2 Combine like terms: -6.05309838 + -2 = -8.05309838 x = -8.05309838 Simplifying x = -8.05309838Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.05309838, -8.05309838}
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