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Simplifying 700 + -220x + x2 = 0 Solving 700 + -220x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-700' to each side of the equation. 700 + -220x + -700 + x2 = 0 + -700 Reorder the terms: 700 + -700 + -220x + x2 = 0 + -700 Combine like terms: 700 + -700 = 0 0 + -220x + x2 = 0 + -700 -220x + x2 = 0 + -700 Combine like terms: 0 + -700 = -700 -220x + x2 = -700 The x term is -220x. Take half its coefficient (-110). Square it (12100) and add it to both sides. Add '12100' to each side of the equation. -220x + 12100 + x2 = -700 + 12100 Reorder the terms: 12100 + -220x + x2 = -700 + 12100 Combine like terms: -700 + 12100 = 11400 12100 + -220x + x2 = 11400 Factor a perfect square on the left side: (x + -110)(x + -110) = 11400 Calculate the square root of the right side: 106.77078252 Break this problem into two subproblems by setting (x + -110) equal to 106.77078252 and -106.77078252.Subproblem 1
x + -110 = 106.77078252 Simplifying x + -110 = 106.77078252 Reorder the terms: -110 + x = 106.77078252 Solving -110 + x = 106.77078252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '110' to each side of the equation. -110 + 110 + x = 106.77078252 + 110 Combine like terms: -110 + 110 = 0 0 + x = 106.77078252 + 110 x = 106.77078252 + 110 Combine like terms: 106.77078252 + 110 = 216.77078252 x = 216.77078252 Simplifying x = 216.77078252Subproblem 2
x + -110 = -106.77078252 Simplifying x + -110 = -106.77078252 Reorder the terms: -110 + x = -106.77078252 Solving -110 + x = -106.77078252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '110' to each side of the equation. -110 + 110 + x = -106.77078252 + 110 Combine like terms: -110 + 110 = 0 0 + x = -106.77078252 + 110 x = -106.77078252 + 110 Combine like terms: -106.77078252 + 110 = 3.22921748 x = 3.22921748 Simplifying x = 3.22921748Solution
The solution to the problem is based on the solutions from the subproblems. x = {216.77078252, 3.22921748}
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