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Simplifying x2 + -49x + 8 = 0 Reorder the terms: 8 + -49x + x2 = 0 Solving 8 + -49x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -49x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -49x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -49x + x2 = 0 + -8 -49x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -49x + x2 = -8 The x term is -49x. Take half its coefficient (-24.5). Square it (600.25) and add it to both sides. Add '600.25' to each side of the equation. -49x + 600.25 + x2 = -8 + 600.25 Reorder the terms: 600.25 + -49x + x2 = -8 + 600.25 Combine like terms: -8 + 600.25 = 592.25 600.25 + -49x + x2 = 592.25 Factor a perfect square on the left side: (x + -24.5)(x + -24.5) = 592.25 Calculate the square root of the right side: 24.336187047 Break this problem into two subproblems by setting (x + -24.5) equal to 24.336187047 and -24.336187047.Subproblem 1
x + -24.5 = 24.336187047 Simplifying x + -24.5 = 24.336187047 Reorder the terms: -24.5 + x = 24.336187047 Solving -24.5 + x = 24.336187047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.5' to each side of the equation. -24.5 + 24.5 + x = 24.336187047 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = 24.336187047 + 24.5 x = 24.336187047 + 24.5 Combine like terms: 24.336187047 + 24.5 = 48.836187047 x = 48.836187047 Simplifying x = 48.836187047Subproblem 2
x + -24.5 = -24.336187047 Simplifying x + -24.5 = -24.336187047 Reorder the terms: -24.5 + x = -24.336187047 Solving -24.5 + x = -24.336187047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.5' to each side of the equation. -24.5 + 24.5 + x = -24.336187047 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = -24.336187047 + 24.5 x = -24.336187047 + 24.5 Combine like terms: -24.336187047 + 24.5 = 0.163812953 x = 0.163812953 Simplifying x = 0.163812953Solution
The solution to the problem is based on the solutions from the subproblems. x = {48.836187047, 0.163812953}
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