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Simplifying x2 + -22x = 57 Reorder the terms: -22x + x2 = 57 Solving -22x + x2 = 57 Solving for variable 'x'. Reorder the terms: -57 + -22x + x2 = 57 + -57 Combine like terms: 57 + -57 = 0 -57 + -22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '57' to each side of the equation. -57 + -22x + 57 + x2 = 0 + 57 Reorder the terms: -57 + 57 + -22x + x2 = 0 + 57 Combine like terms: -57 + 57 = 0 0 + -22x + x2 = 0 + 57 -22x + x2 = 0 + 57 Combine like terms: 0 + 57 = 57 -22x + x2 = 57 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 = 57 + 121 Reorder the terms: 121 + -22x + x2 = 57 + 121 Combine like terms: 57 + 121 = 178 121 + -22x + x2 = 178 Factor a perfect square on the left side: (x + -11)(x + -11) = 178 Calculate the square root of the right side: 13.341664064 Break this problem into two subproblems by setting (x + -11) equal to 13.341664064 and -13.341664064.Subproblem 1
x + -11 = 13.341664064 Simplifying x + -11 = 13.341664064 Reorder the terms: -11 + x = 13.341664064 Solving -11 + x = 13.341664064 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 = 13.341664064 + 11 Combine like terms: -11 + 11 = 0 0 + x = 13.341664064 + 11 x = 13.341664064 + 11 Combine like terms: 13.341664064 + 11 = 24.341664064 x = 24.341664064 Simplifying x = 24.341664064Subproblem 2
x + -11 = -13.341664064 Simplifying x + -11 = -13.341664064 Reorder the terms: -11 + x = -13.341664064 Solving -11 + x = -13.341664064 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 = -13.341664064 + 11 Combine like terms: -11 + 11 = 0 0 + x = -13.341664064 + 11 x = -13.341664064 + 11 Combine like terms: -13.341664064 + 11 = -2.341664064 x = -2.341664064 Simplifying x = -2.341664064Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.341664064, -2.341664064}
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