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Simplifying x2 + 18x + 25 = 0 Reorder the terms: 25 + 18x + x2 = 0 Solving 25 + 18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + 18x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + 18x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 18x + x2 = 0 + -25 18x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 18x + x2 = -25 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = -25 + 81 Reorder the terms: 81 + 18x + x2 = -25 + 81 Combine like terms: -25 + 81 = 56 81 + 18x + x2 = 56 Factor a perfect square on the left side: (x + 9)(x + 9) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (x + 9) equal to 7.483314774 and -7.483314774.Subproblem 1
x + 9 = 7.483314774 Simplifying x + 9 = 7.483314774 Reorder the terms: 9 + x = 7.483314774 Solving 9 + x = 7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 7.483314774 + -9 Combine like terms: 9 + -9 = 0 0 + x = 7.483314774 + -9 x = 7.483314774 + -9 Combine like terms: 7.483314774 + -9 = -1.516685226 x = -1.516685226 Simplifying x = -1.516685226Subproblem 2
x + 9 = -7.483314774 Simplifying x + 9 = -7.483314774 Reorder the terms: 9 + x = -7.483314774 Solving 9 + x = -7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -7.483314774 + -9 Combine like terms: 9 + -9 = 0 0 + x = -7.483314774 + -9 x = -7.483314774 + -9 Combine like terms: -7.483314774 + -9 = -16.483314774 x = -16.483314774 Simplifying x = -16.483314774Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.516685226, -16.483314774}
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