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Simplifying x2 + 62x + 63 = 0 Reorder the terms: 63 + 62x + x2 = 0 Solving 63 + 62x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-63' to each side of the equation. 63 + 62x + -63 + x2 = 0 + -63 Reorder the terms: 63 + -63 + 62x + x2 = 0 + -63 Combine like terms: 63 + -63 = 0 0 + 62x + x2 = 0 + -63 62x + x2 = 0 + -63 Combine like terms: 0 + -63 = -63 62x + x2 = -63 The x term is 62x. Take half its coefficient (31). Square it (961) and add it to both sides. Add '961' to each side of the equation. 62x + 961 + x2 = -63 + 961 Reorder the terms: 961 + 62x + x2 = -63 + 961 Combine like terms: -63 + 961 = 898 961 + 62x + x2 = 898 Factor a perfect square on the left side: (x + 31)(x + 31) = 898 Calculate the square root of the right side: 29.966648128 Break this problem into two subproblems by setting (x + 31) equal to 29.966648128 and -29.966648128.Subproblem 1
x + 31 = 29.966648128 Simplifying x + 31 = 29.966648128 Reorder the terms: 31 + x = 29.966648128 Solving 31 + x = 29.966648128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + x = 29.966648128 + -31 Combine like terms: 31 + -31 = 0 0 + x = 29.966648128 + -31 x = 29.966648128 + -31 Combine like terms: 29.966648128 + -31 = -1.033351872 x = -1.033351872 Simplifying x = -1.033351872Subproblem 2
x + 31 = -29.966648128 Simplifying x + 31 = -29.966648128 Reorder the terms: 31 + x = -29.966648128 Solving 31 + x = -29.966648128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + x = -29.966648128 + -31 Combine like terms: 31 + -31 = 0 0 + x = -29.966648128 + -31 x = -29.966648128 + -31 Combine like terms: -29.966648128 + -31 = -60.966648128 x = -60.966648128 Simplifying x = -60.966648128Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.033351872, -60.966648128}
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