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Simplifying x2 + 61x = 60 Reorder the terms: 61x + x2 = 60 Solving 61x + x2 = 60 Solving for variable 'x'. Reorder the terms: -60 + 61x + x2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + 61x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 61x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + 61x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 61x + x2 = 0 + 60 61x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 61x + x2 = 60 The x term is 61x. Take half its coefficient (30.5). Square it (930.25) and add it to both sides. Add '930.25' to each side of the equation. 61x + 930.25 + x2 = 60 + 930.25 Reorder the terms: 930.25 + 61x + x2 = 60 + 930.25 Combine like terms: 60 + 930.25 = 990.25 930.25 + 61x + x2 = 990.25 Factor a perfect square on the left side: (x + 30.5)(x + 30.5) = 990.25 Calculate the square root of the right side: 31.468237955 Break this problem into two subproblems by setting (x + 30.5) equal to 31.468237955 and -31.468237955.Subproblem 1
x + 30.5 = 31.468237955 Simplifying x + 30.5 = 31.468237955 Reorder the terms: 30.5 + x = 31.468237955 Solving 30.5 + x = 31.468237955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30.5' to each side of the equation. 30.5 + -30.5 + x = 31.468237955 + -30.5 Combine like terms: 30.5 + -30.5 = 0.0 0.0 + x = 31.468237955 + -30.5 x = 31.468237955 + -30.5 Combine like terms: 31.468237955 + -30.5 = 0.968237955 x = 0.968237955 Simplifying x = 0.968237955Subproblem 2
x + 30.5 = -31.468237955 Simplifying x + 30.5 = -31.468237955 Reorder the terms: 30.5 + x = -31.468237955 Solving 30.5 + x = -31.468237955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30.5' to each side of the equation. 30.5 + -30.5 + x = -31.468237955 + -30.5 Combine like terms: 30.5 + -30.5 = 0.0 0.0 + x = -31.468237955 + -30.5 x = -31.468237955 + -30.5 Combine like terms: -31.468237955 + -30.5 = -61.968237955 x = -61.968237955 Simplifying x = -61.968237955Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.968237955, -61.968237955}
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