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Simplifying x2 + -22x + -35 = 0 Reorder the terms: -35 + -22x + x2 = 0 Solving -35 + -22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -22x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + -22x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -22x + x2 = 0 + 35 -22x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 -22x + x2 = 35 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 = 35 + 121 Reorder the terms: 121 + -22x + x2 = 35 + 121 Combine like terms: 35 + 121 = 156 121 + -22x + x2 = 156 Factor a perfect square on the left side: (x + -11)(x + -11) = 156 Calculate the square root of the right side: 12.489995997 Break this problem into two subproblems by setting (x + -11) equal to 12.489995997 and -12.489995997.Subproblem 1
x + -11 = 12.489995997 Simplifying x + -11 = 12.489995997 Reorder the terms: -11 + x = 12.489995997 Solving -11 + x = 12.489995997 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 = 12.489995997 + 11 Combine like terms: -11 + 11 = 0 0 + x = 12.489995997 + 11 x = 12.489995997 + 11 Combine like terms: 12.489995997 + 11 = 23.489995997 x = 23.489995997 Simplifying x = 23.489995997Subproblem 2
x + -11 = -12.489995997 Simplifying x + -11 = -12.489995997 Reorder the terms: -11 + x = -12.489995997 Solving -11 + x = -12.489995997 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 = -12.489995997 + 11 Combine like terms: -11 + 11 = 0 0 + x = -12.489995997 + 11 x = -12.489995997 + 11 Combine like terms: -12.489995997 + 11 = -1.489995997 x = -1.489995997 Simplifying x = -1.489995997Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.489995997, -1.489995997}
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