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Simplifying x2 + -49x + -455 = 0 Reorder the terms: -455 + -49x + x2 = 0 Solving -455 + -49x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '455' to each side of the equation. -455 + -49x + 455 + x2 = 0 + 455 Reorder the terms: -455 + 455 + -49x + x2 = 0 + 455 Combine like terms: -455 + 455 = 0 0 + -49x + x2 = 0 + 455 -49x + x2 = 0 + 455 Combine like terms: 0 + 455 = 455 -49x + x2 = 455 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 = 455 + 600.25 Reorder the terms: 600.25 + -49x + x2 = 455 + 600.25 Combine like terms: 455 + 600.25 = 1055.25 600.25 + -49x + x2 = 1055.25 Factor a perfect square on the left side: (x + -24.5)(x + -24.5) = 1055.25 Calculate the square root of the right side: 32.484611742 Break this problem into two subproblems by setting (x + -24.5) equal to 32.484611742 and -32.484611742.Subproblem 1
x + -24.5 = 32.484611742 Simplifying x + -24.5 = 32.484611742 Reorder the terms: -24.5 + x = 32.484611742 Solving -24.5 + x = 32.484611742 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 = 32.484611742 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = 32.484611742 + 24.5 x = 32.484611742 + 24.5 Combine like terms: 32.484611742 + 24.5 = 56.984611742 x = 56.984611742 Simplifying x = 56.984611742Subproblem 2
x + -24.5 = -32.484611742 Simplifying x + -24.5 = -32.484611742 Reorder the terms: -24.5 + x = -32.484611742 Solving -24.5 + x = -32.484611742 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 = -32.484611742 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = -32.484611742 + 24.5 x = -32.484611742 + 24.5 Combine like terms: -32.484611742 + 24.5 = -7.984611742 x = -7.984611742 Simplifying x = -7.984611742Solution
The solution to the problem is based on the solutions from the subproblems. x = {56.984611742, -7.984611742}
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