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Simplifying x2 + 49x + 410 = 0 Reorder the terms: 410 + 49x + x2 = 0 Solving 410 + 49x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-410' to each side of the equation. 410 + 49x + -410 + x2 = 0 + -410 Reorder the terms: 410 + -410 + 49x + x2 = 0 + -410 Combine like terms: 410 + -410 = 0 0 + 49x + x2 = 0 + -410 49x + x2 = 0 + -410 Combine like terms: 0 + -410 = -410 49x + x2 = -410 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 = -410 + 600.25 Reorder the terms: 600.25 + 49x + x2 = -410 + 600.25 Combine like terms: -410 + 600.25 = 190.25 600.25 + 49x + x2 = 190.25 Factor a perfect square on the left side: (x + 24.5)(x + 24.5) = 190.25 Calculate the square root of the right side: 13.793114224 Break this problem into two subproblems by setting (x + 24.5) equal to 13.793114224 and -13.793114224.Subproblem 1
x + 24.5 = 13.793114224 Simplifying x + 24.5 = 13.793114224 Reorder the terms: 24.5 + x = 13.793114224 Solving 24.5 + x = 13.793114224 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 = 13.793114224 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + x = 13.793114224 + -24.5 x = 13.793114224 + -24.5 Combine like terms: 13.793114224 + -24.5 = -10.706885776 x = -10.706885776 Simplifying x = -10.706885776Subproblem 2
x + 24.5 = -13.793114224 Simplifying x + 24.5 = -13.793114224 Reorder the terms: 24.5 + x = -13.793114224 Solving 24.5 + x = -13.793114224 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 = -13.793114224 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + x = -13.793114224 + -24.5 x = -13.793114224 + -24.5 Combine like terms: -13.793114224 + -24.5 = -38.293114224 x = -38.293114224 Simplifying x = -38.293114224Solution
The solution to the problem is based on the solutions from the subproblems. x = {-10.706885776, -38.293114224}
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