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Simplifying x2 + -49x + -130 = 0 Reorder the terms: -130 + -49x + x2 = 0 Solving -130 + -49x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '130' to each side of the equation. -130 + -49x + 130 + x2 = 0 + 130 Reorder the terms: -130 + 130 + -49x + x2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + -49x + x2 = 0 + 130 -49x + x2 = 0 + 130 Combine like terms: 0 + 130 = 130 -49x + x2 = 130 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 = 130 + 600.25 Reorder the terms: 600.25 + -49x + x2 = 130 + 600.25 Combine like terms: 130 + 600.25 = 730.25 600.25 + -49x + x2 = 730.25 Factor a perfect square on the left side: (x + -24.5)(x + -24.5) = 730.25 Calculate the square root of the right side: 27.023138234 Break this problem into two subproblems by setting (x + -24.5) equal to 27.023138234 and -27.023138234.Subproblem 1
x + -24.5 = 27.023138234 Simplifying x + -24.5 = 27.023138234 Reorder the terms: -24.5 + x = 27.023138234 Solving -24.5 + x = 27.023138234 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 = 27.023138234 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = 27.023138234 + 24.5 x = 27.023138234 + 24.5 Combine like terms: 27.023138234 + 24.5 = 51.523138234 x = 51.523138234 Simplifying x = 51.523138234Subproblem 2
x + -24.5 = -27.023138234 Simplifying x + -24.5 = -27.023138234 Reorder the terms: -24.5 + x = -27.023138234 Solving -24.5 + x = -27.023138234 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 = -27.023138234 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = -27.023138234 + 24.5 x = -27.023138234 + 24.5 Combine like terms: -27.023138234 + 24.5 = -2.523138234 x = -2.523138234 Simplifying x = -2.523138234Solution
The solution to the problem is based on the solutions from the subproblems. x = {51.523138234, -2.523138234}
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