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Simplifying x2 + 22x + 90 = 0 Reorder the terms: 90 + 22x + x2 = 0 Solving 90 + 22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-90' to each side of the equation. 90 + 22x + -90 + x2 = 0 + -90 Reorder the terms: 90 + -90 + 22x + x2 = 0 + -90 Combine like terms: 90 + -90 = 0 0 + 22x + x2 = 0 + -90 22x + x2 = 0 + -90 Combine like terms: 0 + -90 = -90 22x + x2 = -90 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 = -90 + 121 Reorder the terms: 121 + 22x + x2 = -90 + 121 Combine like terms: -90 + 121 = 31 121 + 22x + x2 = 31 Factor a perfect square on the left side: (x + 11)(x + 11) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (x + 11) equal to 5.567764363 and -5.567764363.Subproblem 1
x + 11 = 5.567764363 Simplifying x + 11 = 5.567764363 Reorder the terms: 11 + x = 5.567764363 Solving 11 + x = 5.567764363 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 = 5.567764363 + -11 Combine like terms: 11 + -11 = 0 0 + x = 5.567764363 + -11 x = 5.567764363 + -11 Combine like terms: 5.567764363 + -11 = -5.432235637 x = -5.432235637 Simplifying x = -5.432235637Subproblem 2
x + 11 = -5.567764363 Simplifying x + 11 = -5.567764363 Reorder the terms: 11 + x = -5.567764363 Solving 11 + x = -5.567764363 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 = -5.567764363 + -11 Combine like terms: 11 + -11 = 0 0 + x = -5.567764363 + -11 x = -5.567764363 + -11 Combine like terms: -5.567764363 + -11 = -16.567764363 x = -16.567764363 Simplifying x = -16.567764363Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.432235637, -16.567764363}
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