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Simplifying x2 + 49x + -380 = 0 Reorder the terms: -380 + 49x + x2 = 0 Solving -380 + 49x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '380' to each side of the equation. -380 + 49x + 380 + x2 = 0 + 380 Reorder the terms: -380 + 380 + 49x + x2 = 0 + 380 Combine like terms: -380 + 380 = 0 0 + 49x + x2 = 0 + 380 49x + x2 = 0 + 380 Combine like terms: 0 + 380 = 380 49x + x2 = 380 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 = 380 + 600.25 Reorder the terms: 600.25 + 49x + x2 = 380 + 600.25 Combine like terms: 380 + 600.25 = 980.25 600.25 + 49x + x2 = 980.25 Factor a perfect square on the left side: (x + 24.5)(x + 24.5) = 980.25 Calculate the square root of the right side: 31.308944409 Break this problem into two subproblems by setting (x + 24.5) equal to 31.308944409 and -31.308944409.Subproblem 1
x + 24.5 = 31.308944409 Simplifying x + 24.5 = 31.308944409 Reorder the terms: 24.5 + x = 31.308944409 Solving 24.5 + x = 31.308944409 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 = 31.308944409 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + x = 31.308944409 + -24.5 x = 31.308944409 + -24.5 Combine like terms: 31.308944409 + -24.5 = 6.808944409 x = 6.808944409 Simplifying x = 6.808944409Subproblem 2
x + 24.5 = -31.308944409 Simplifying x + 24.5 = -31.308944409 Reorder the terms: 24.5 + x = -31.308944409 Solving 24.5 + x = -31.308944409 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 = -31.308944409 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + x = -31.308944409 + -24.5 x = -31.308944409 + -24.5 Combine like terms: -31.308944409 + -24.5 = -55.808944409 x = -55.808944409 Simplifying x = -55.808944409Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.808944409, -55.808944409}
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