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Simplifying x2 + 10x + 18x + 5 = 0 Reorder the terms: 5 + 10x + 18x + x2 = 0 Combine like terms: 10x + 18x = 28x 5 + 28x + x2 = 0 Solving 5 + 28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 28x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 28x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 28x + x2 = 0 + -5 28x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 28x + x2 = -5 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = -5 + 196 Reorder the terms: 196 + 28x + x2 = -5 + 196 Combine like terms: -5 + 196 = 191 196 + 28x + x2 = 191 Factor a perfect square on the left side: (x + 14)(x + 14) = 191 Calculate the square root of the right side: 13.820274961 Break this problem into two subproblems by setting (x + 14) equal to 13.820274961 and -13.820274961.Subproblem 1
x + 14 = 13.820274961 Simplifying x + 14 = 13.820274961 Reorder the terms: 14 + x = 13.820274961 Solving 14 + x = 13.820274961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 13.820274961 + -14 Combine like terms: 14 + -14 = 0 0 + x = 13.820274961 + -14 x = 13.820274961 + -14 Combine like terms: 13.820274961 + -14 = -0.179725039 x = -0.179725039 Simplifying x = -0.179725039Subproblem 2
x + 14 = -13.820274961 Simplifying x + 14 = -13.820274961 Reorder the terms: 14 + x = -13.820274961 Solving 14 + x = -13.820274961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -13.820274961 + -14 Combine like terms: 14 + -14 = 0 0 + x = -13.820274961 + -14 x = -13.820274961 + -14 Combine like terms: -13.820274961 + -14 = -27.820274961 x = -27.820274961 Simplifying x = -27.820274961Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.179725039, -27.820274961}
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