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Simplifying x2 + 32x + 84 = 0 Reorder the terms: 84 + 32x + x2 = 0 Solving 84 + 32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-84' to each side of the equation. 84 + 32x + -84 + x2 = 0 + -84 Reorder the terms: 84 + -84 + 32x + x2 = 0 + -84 Combine like terms: 84 + -84 = 0 0 + 32x + x2 = 0 + -84 32x + x2 = 0 + -84 Combine like terms: 0 + -84 = -84 32x + x2 = -84 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 = -84 + 256 Reorder the terms: 256 + 32x + x2 = -84 + 256 Combine like terms: -84 + 256 = 172 256 + 32x + x2 = 172 Factor a perfect square on the left side: (x + 16)(x + 16) = 172 Calculate the square root of the right side: 13.114877049 Break this problem into two subproblems by setting (x + 16) equal to 13.114877049 and -13.114877049.Subproblem 1
x + 16 = 13.114877049 Simplifying x + 16 = 13.114877049 Reorder the terms: 16 + x = 13.114877049 Solving 16 + x = 13.114877049 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 = 13.114877049 + -16 Combine like terms: 16 + -16 = 0 0 + x = 13.114877049 + -16 x = 13.114877049 + -16 Combine like terms: 13.114877049 + -16 = -2.885122951 x = -2.885122951 Simplifying x = -2.885122951Subproblem 2
x + 16 = -13.114877049 Simplifying x + 16 = -13.114877049 Reorder the terms: 16 + x = -13.114877049 Solving 16 + x = -13.114877049 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 = -13.114877049 + -16 Combine like terms: 16 + -16 = 0 0 + x = -13.114877049 + -16 x = -13.114877049 + -16 Combine like terms: -13.114877049 + -16 = -29.114877049 x = -29.114877049 Simplifying x = -29.114877049Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.885122951, -29.114877049}
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