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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 = 145.25 600.25 + -49x + x2 = 145.25 Factor a perfect square on the left side: (x + -24.5)(x + -24.5) = 145.25 Calculate the square root of the right side: 12.051970793 Break this problem into two subproblems by setting (x + -24.5) equal to 12.051970793 and -12.051970793.Subproblem 1
x + -24.5 = 12.051970793 Simplifying x + -24.5 = 12.051970793 Reorder the terms: -24.5 + x = 12.051970793 Solving -24.5 + x = 12.051970793 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 = 12.051970793 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = 12.051970793 + 24.5 x = 12.051970793 + 24.5 Combine like terms: 12.051970793 + 24.5 = 36.551970793 x = 36.551970793 Simplifying x = 36.551970793Subproblem 2
x + -24.5 = -12.051970793 Simplifying x + -24.5 = -12.051970793 Reorder the terms: -24.5 + x = -12.051970793 Solving -24.5 + x = -12.051970793 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 = -12.051970793 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = -12.051970793 + 24.5 x = -12.051970793 + 24.5 Combine like terms: -12.051970793 + 24.5 = 12.448029207 x = 12.448029207 Simplifying x = 12.448029207Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.551970793, 12.448029207}
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