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Simplifying x2 + 24x + 90 = 0 Reorder the terms: 90 + 24x + x2 = 0 Solving 90 + 24x + 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 + 24x + -90 + x2 = 0 + -90 Reorder the terms: 90 + -90 + 24x + x2 = 0 + -90 Combine like terms: 90 + -90 = 0 0 + 24x + x2 = 0 + -90 24x + x2 = 0 + -90 Combine like terms: 0 + -90 = -90 24x + x2 = -90 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = -90 + 144 Reorder the terms: 144 + 24x + x2 = -90 + 144 Combine like terms: -90 + 144 = 54 144 + 24x + x2 = 54 Factor a perfect square on the left side: (x + 12)(x + 12) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (x + 12) equal to 7.348469228 and -7.348469228.Subproblem 1
x + 12 = 7.348469228 Simplifying x + 12 = 7.348469228 Reorder the terms: 12 + x = 7.348469228 Solving 12 + x = 7.348469228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 7.348469228 + -12 Combine like terms: 12 + -12 = 0 0 + x = 7.348469228 + -12 x = 7.348469228 + -12 Combine like terms: 7.348469228 + -12 = -4.651530772 x = -4.651530772 Simplifying x = -4.651530772Subproblem 2
x + 12 = -7.348469228 Simplifying x + 12 = -7.348469228 Reorder the terms: 12 + x = -7.348469228 Solving 12 + x = -7.348469228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -7.348469228 + -12 Combine like terms: 12 + -12 = 0 0 + x = -7.348469228 + -12 x = -7.348469228 + -12 Combine like terms: -7.348469228 + -12 = -19.348469228 x = -19.348469228 Simplifying x = -19.348469228Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.651530772, -19.348469228}
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