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Simplifying x2 + 64x + 225 = 0 Reorder the terms: 225 + 64x + x2 = 0 Solving 225 + 64x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-225' to each side of the equation. 225 + 64x + -225 + x2 = 0 + -225 Reorder the terms: 225 + -225 + 64x + x2 = 0 + -225 Combine like terms: 225 + -225 = 0 0 + 64x + x2 = 0 + -225 64x + x2 = 0 + -225 Combine like terms: 0 + -225 = -225 64x + x2 = -225 The x term is 64x. Take half its coefficient (32). Square it (1024) and add it to both sides. Add '1024' to each side of the equation. 64x + 1024 + x2 = -225 + 1024 Reorder the terms: 1024 + 64x + x2 = -225 + 1024 Combine like terms: -225 + 1024 = 799 1024 + 64x + x2 = 799 Factor a perfect square on the left side: (x + 32)(x + 32) = 799 Calculate the square root of the right side: 28.26658805 Break this problem into two subproblems by setting (x + 32) equal to 28.26658805 and -28.26658805.Subproblem 1
x + 32 = 28.26658805 Simplifying x + 32 = 28.26658805 Reorder the terms: 32 + x = 28.26658805 Solving 32 + x = 28.26658805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + x = 28.26658805 + -32 Combine like terms: 32 + -32 = 0 0 + x = 28.26658805 + -32 x = 28.26658805 + -32 Combine like terms: 28.26658805 + -32 = -3.73341195 x = -3.73341195 Simplifying x = -3.73341195Subproblem 2
x + 32 = -28.26658805 Simplifying x + 32 = -28.26658805 Reorder the terms: 32 + x = -28.26658805 Solving 32 + x = -28.26658805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + x = -28.26658805 + -32 Combine like terms: 32 + -32 = 0 0 + x = -28.26658805 + -32 x = -28.26658805 + -32 Combine like terms: -28.26658805 + -32 = -60.26658805 x = -60.26658805 Simplifying x = -60.26658805Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.73341195, -60.26658805}
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