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Simplifying x2 + -50x + -54 = 0 Reorder the terms: -54 + -50x + x2 = 0 Solving -54 + -50x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + -50x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + -50x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + -50x + x2 = 0 + 54 -50x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 -50x + x2 = 54 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = 54 + 625 Reorder the terms: 625 + -50x + x2 = 54 + 625 Combine like terms: 54 + 625 = 679 625 + -50x + x2 = 679 Factor a perfect square on the left side: (x + -25)(x + -25) = 679 Calculate the square root of the right side: 26.057628442 Break this problem into two subproblems by setting (x + -25) equal to 26.057628442 and -26.057628442.Subproblem 1
x + -25 = 26.057628442 Simplifying x + -25 = 26.057628442 Reorder the terms: -25 + x = 26.057628442 Solving -25 + x = 26.057628442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 26.057628442 + 25 Combine like terms: -25 + 25 = 0 0 + x = 26.057628442 + 25 x = 26.057628442 + 25 Combine like terms: 26.057628442 + 25 = 51.057628442 x = 51.057628442 Simplifying x = 51.057628442Subproblem 2
x + -25 = -26.057628442 Simplifying x + -25 = -26.057628442 Reorder the terms: -25 + x = -26.057628442 Solving -25 + x = -26.057628442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -26.057628442 + 25 Combine like terms: -25 + 25 = 0 0 + x = -26.057628442 + 25 x = -26.057628442 + 25 Combine like terms: -26.057628442 + 25 = -1.057628442 x = -1.057628442 Simplifying x = -1.057628442Solution
The solution to the problem is based on the solutions from the subproblems. x = {51.057628442, -1.057628442}
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