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Simplifying x2 + 10x + 14 = 0 Reorder the terms: 14 + 10x + x2 = 0 Solving 14 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 10x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + 10x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 10x + x2 = 0 + -14 10x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 10x + x2 = -14 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -14 + 25 Reorder the terms: 25 + 10x + x2 = -14 + 25 Combine like terms: -14 + 25 = 11 25 + 10x + x2 = 11 Factor a perfect square on the left side: (x + 5)(x + 5) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + 5) equal to 3.31662479 and -3.31662479.Subproblem 1
x + 5 = 3.31662479 Simplifying x + 5 = 3.31662479 Reorder the terms: 5 + x = 3.31662479 Solving 5 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 3.31662479 + -5 Combine like terms: 5 + -5 = 0 0 + x = 3.31662479 + -5 x = 3.31662479 + -5 Combine like terms: 3.31662479 + -5 = -1.68337521 x = -1.68337521 Simplifying x = -1.68337521Subproblem 2
x + 5 = -3.31662479 Simplifying x + 5 = -3.31662479 Reorder the terms: 5 + x = -3.31662479 Solving 5 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -3.31662479 + -5 Combine like terms: 5 + -5 = 0 0 + x = -3.31662479 + -5 x = -3.31662479 + -5 Combine like terms: -3.31662479 + -5 = -8.31662479 x = -8.31662479 Simplifying x = -8.31662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.68337521, -8.31662479}
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