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Simplifying x2 + -22x + 84 = 0 Reorder the terms: 84 + -22x + x2 = 0 Solving 84 + -22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-84' to each side of the equation. 84 + -22x + -84 + x2 = 0 + -84 Reorder the terms: 84 + -84 + -22x + x2 = 0 + -84 Combine like terms: 84 + -84 = 0 0 + -22x + x2 = 0 + -84 -22x + x2 = 0 + -84 Combine like terms: 0 + -84 = -84 -22x + x2 = -84 The x term is -22x. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x + 121 + x2 = -84 + 121 Reorder the terms: 121 + -22x + x2 = -84 + 121 Combine like terms: -84 + 121 = 37 121 + -22x + x2 = 37 Factor a perfect square on the left side: (x + -11)(x + -11) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (x + -11) equal to 6.08276253 and -6.08276253.Subproblem 1
x + -11 = 6.08276253 Simplifying x + -11 = 6.08276253 Reorder the terms: -11 + x = 6.08276253 Solving -11 + x = 6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 6.08276253 + 11 Combine like terms: -11 + 11 = 0 0 + x = 6.08276253 + 11 x = 6.08276253 + 11 Combine like terms: 6.08276253 + 11 = 17.08276253 x = 17.08276253 Simplifying x = 17.08276253Subproblem 2
x + -11 = -6.08276253 Simplifying x + -11 = -6.08276253 Reorder the terms: -11 + x = -6.08276253 Solving -11 + x = -6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -6.08276253 + 11 Combine like terms: -11 + 11 = 0 0 + x = -6.08276253 + 11 x = -6.08276253 + 11 Combine like terms: -6.08276253 + 11 = 4.91723747 x = 4.91723747 Simplifying x = 4.91723747Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.08276253, 4.91723747}
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