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Simplifying x2 + -22x + 97 = 0 Reorder the terms: 97 + -22x + x2 = 0 Solving 97 + -22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-97' to each side of the equation. 97 + -22x + -97 + x2 = 0 + -97 Reorder the terms: 97 + -97 + -22x + x2 = 0 + -97 Combine like terms: 97 + -97 = 0 0 + -22x + x2 = 0 + -97 -22x + x2 = 0 + -97 Combine like terms: 0 + -97 = -97 -22x + x2 = -97 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 = -97 + 121 Reorder the terms: 121 + -22x + x2 = -97 + 121 Combine like terms: -97 + 121 = 24 121 + -22x + x2 = 24 Factor a perfect square on the left side: (x + -11)(x + -11) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (x + -11) equal to 4.898979486 and -4.898979486.Subproblem 1
x + -11 = 4.898979486 Simplifying x + -11 = 4.898979486 Reorder the terms: -11 + x = 4.898979486 Solving -11 + x = 4.898979486 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 = 4.898979486 + 11 Combine like terms: -11 + 11 = 0 0 + x = 4.898979486 + 11 x = 4.898979486 + 11 Combine like terms: 4.898979486 + 11 = 15.898979486 x = 15.898979486 Simplifying x = 15.898979486Subproblem 2
x + -11 = -4.898979486 Simplifying x + -11 = -4.898979486 Reorder the terms: -11 + x = -4.898979486 Solving -11 + x = -4.898979486 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 = -4.898979486 + 11 Combine like terms: -11 + 11 = 0 0 + x = -4.898979486 + 11 x = -4.898979486 + 11 Combine like terms: -4.898979486 + 11 = 6.101020514 x = 6.101020514 Simplifying x = 6.101020514Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.898979486, 6.101020514}
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