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Simplifying x2 + 22x + -285 = 0 Reorder the terms: -285 + 22x + x2 = 0 Solving -285 + 22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '285' to each side of the equation. -285 + 22x + 285 + x2 = 0 + 285 Reorder the terms: -285 + 285 + 22x + x2 = 0 + 285 Combine like terms: -285 + 285 = 0 0 + 22x + x2 = 0 + 285 22x + x2 = 0 + 285 Combine like terms: 0 + 285 = 285 22x + x2 = 285 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 = 285 + 121 Reorder the terms: 121 + 22x + x2 = 285 + 121 Combine like terms: 285 + 121 = 406 121 + 22x + x2 = 406 Factor a perfect square on the left side: (x + 11)(x + 11) = 406 Calculate the square root of the right side: 20.14944168 Break this problem into two subproblems by setting (x + 11) equal to 20.14944168 and -20.14944168.Subproblem 1
x + 11 = 20.14944168 Simplifying x + 11 = 20.14944168 Reorder the terms: 11 + x = 20.14944168 Solving 11 + x = 20.14944168 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 = 20.14944168 + -11 Combine like terms: 11 + -11 = 0 0 + x = 20.14944168 + -11 x = 20.14944168 + -11 Combine like terms: 20.14944168 + -11 = 9.14944168 x = 9.14944168 Simplifying x = 9.14944168Subproblem 2
x + 11 = -20.14944168 Simplifying x + 11 = -20.14944168 Reorder the terms: 11 + x = -20.14944168 Solving 11 + x = -20.14944168 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 = -20.14944168 + -11 Combine like terms: 11 + -11 = 0 0 + x = -20.14944168 + -11 x = -20.14944168 + -11 Combine like terms: -20.14944168 + -11 = -31.14944168 x = -31.14944168 Simplifying x = -31.14944168Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.14944168, -31.14944168}
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