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Simplifying x2 + 15x + 25 = 0 Reorder the terms: 25 + 15x + x2 = 0 Solving 25 + 15x + 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 + 15x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + 15x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 15x + x2 = 0 + -25 15x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 15x + x2 = -25 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = -25 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -25 + 56.25 Combine like terms: -25 + 56.25 = 31.25 56.25 + 15x + x2 = 31.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (x + 7.5) equal to 5.590169944 and -5.590169944.Subproblem 1
x + 7.5 = 5.590169944 Simplifying x + 7.5 = 5.590169944 Reorder the terms: 7.5 + x = 5.590169944 Solving 7.5 + x = 5.590169944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 5.590169944 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 5.590169944 + -7.5 x = 5.590169944 + -7.5 Combine like terms: 5.590169944 + -7.5 = -1.909830056 x = -1.909830056 Simplifying x = -1.909830056Subproblem 2
x + 7.5 = -5.590169944 Simplifying x + 7.5 = -5.590169944 Reorder the terms: 7.5 + x = -5.590169944 Solving 7.5 + x = -5.590169944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -5.590169944 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -5.590169944 + -7.5 x = -5.590169944 + -7.5 Combine like terms: -5.590169944 + -7.5 = -13.090169944 x = -13.090169944 Simplifying x = -13.090169944Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.909830056, -13.090169944}
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