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Simplifying 0 = x2 + -22x + -25 Reorder the terms: 0 = -25 + -22x + x2 Solving 0 = -25 + -22x + x2 Solving for variable 'x'. Combine like terms: 0 + 25 = 25 25 + 22x + -1x2 = -25 + -22x + x2 + 25 + 22x + -1x2 Reorder the terms: 25 + 22x + -1x2 = -25 + 25 + -22x + 22x + x2 + -1x2 Combine like terms: -25 + 25 = 0 25 + 22x + -1x2 = 0 + -22x + 22x + x2 + -1x2 25 + 22x + -1x2 = -22x + 22x + x2 + -1x2 Combine like terms: -22x + 22x = 0 25 + 22x + -1x2 = 0 + x2 + -1x2 25 + 22x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 25 + 22x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -25 + -22x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -22x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + -22x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -22x + x2 = 0 + 25 -22x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 -22x + x2 = 25 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 = 25 + 121 Reorder the terms: 121 + -22x + x2 = 25 + 121 Combine like terms: 25 + 121 = 146 121 + -22x + x2 = 146 Factor a perfect square on the left side: (x + -11)(x + -11) = 146 Calculate the square root of the right side: 12.083045974 Break this problem into two subproblems by setting (x + -11) equal to 12.083045974 and -12.083045974.Subproblem 1
x + -11 = 12.083045974 Simplifying x + -11 = 12.083045974 Reorder the terms: -11 + x = 12.083045974 Solving -11 + x = 12.083045974 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 = 12.083045974 + 11 Combine like terms: -11 + 11 = 0 0 + x = 12.083045974 + 11 x = 12.083045974 + 11 Combine like terms: 12.083045974 + 11 = 23.083045974 x = 23.083045974 Simplifying x = 23.083045974Subproblem 2
x + -11 = -12.083045974 Simplifying x + -11 = -12.083045974 Reorder the terms: -11 + x = -12.083045974 Solving -11 + x = -12.083045974 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 = -12.083045974 + 11 Combine like terms: -11 + 11 = 0 0 + x = -12.083045974 + 11 x = -12.083045974 + 11 Combine like terms: -12.083045974 + 11 = -1.083045974 x = -1.083045974 Simplifying x = -1.083045974Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.083045974, -1.083045974}
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