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Simplifying x2 + -62x + -9 = 0 Reorder the terms: -9 + -62x + x2 = 0 Solving -9 + -62x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -62x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -62x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -62x + x2 = 0 + 9 -62x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -62x + x2 = 9 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 = 9 + 961 Reorder the terms: 961 + -62x + x2 = 9 + 961 Combine like terms: 9 + 961 = 970 961 + -62x + x2 = 970 Factor a perfect square on the left side: (x + -31)(x + -31) = 970 Calculate the square root of the right side: 31.144823005 Break this problem into two subproblems by setting (x + -31) equal to 31.144823005 and -31.144823005.Subproblem 1
x + -31 = 31.144823005 Simplifying x + -31 = 31.144823005 Reorder the terms: -31 + x = 31.144823005 Solving -31 + x = 31.144823005 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 = 31.144823005 + 31 Combine like terms: -31 + 31 = 0 0 + x = 31.144823005 + 31 x = 31.144823005 + 31 Combine like terms: 31.144823005 + 31 = 62.144823005 x = 62.144823005 Simplifying x = 62.144823005Subproblem 2
x + -31 = -31.144823005 Simplifying x + -31 = -31.144823005 Reorder the terms: -31 + x = -31.144823005 Solving -31 + x = -31.144823005 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 = -31.144823005 + 31 Combine like terms: -31 + 31 = 0 0 + x = -31.144823005 + 31 x = -31.144823005 + 31 Combine like terms: -31.144823005 + 31 = -0.144823005 x = -0.144823005 Simplifying x = -0.144823005Solution
The solution to the problem is based on the solutions from the subproblems. x = {62.144823005, -0.144823005}
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