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Simplifying x(x + 32) = 60 Reorder the terms: x(32 + x) = 60 (32 * x + x * x) = 60 (32x + x2) = 60 Solving 32x + x2 = 60 Solving for variable 'x'. Reorder the terms: -60 + 32x + x2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + 32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 32x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + 32x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 32x + x2 = 0 + 60 32x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 32x + x2 = 60 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = 60 + 256 Reorder the terms: 256 + 32x + x2 = 60 + 256 Combine like terms: 60 + 256 = 316 256 + 32x + x2 = 316 Factor a perfect square on the left side: (x + 16)(x + 16) = 316 Calculate the square root of the right side: 17.776388835 Break this problem into two subproblems by setting (x + 16) equal to 17.776388835 and -17.776388835.Subproblem 1
x + 16 = 17.776388835 Simplifying x + 16 = 17.776388835 Reorder the terms: 16 + x = 17.776388835 Solving 16 + x = 17.776388835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 17.776388835 + -16 Combine like terms: 16 + -16 = 0 0 + x = 17.776388835 + -16 x = 17.776388835 + -16 Combine like terms: 17.776388835 + -16 = 1.776388835 x = 1.776388835 Simplifying x = 1.776388835Subproblem 2
x + 16 = -17.776388835 Simplifying x + 16 = -17.776388835 Reorder the terms: 16 + x = -17.776388835 Solving 16 + x = -17.776388835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -17.776388835 + -16 Combine like terms: 16 + -16 = 0 0 + x = -17.776388835 + -16 x = -17.776388835 + -16 Combine like terms: -17.776388835 + -16 = -33.776388835 x = -33.776388835 Simplifying x = -33.776388835Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.776388835, -33.776388835}
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