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Simplifying x * x + 10x + 13 = 0 Multiply x * x x2 + 10x + 13 = 0 Reorder the terms: 13 + 10x + x2 = 0 Solving 13 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + 10x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + 10x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 10x + x2 = 0 + -13 10x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 10x + x2 = -13 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 = -13 + 25 Reorder the terms: 25 + 10x + x2 = -13 + 25 Combine like terms: -13 + 25 = 12 25 + 10x + x2 = 12 Factor a perfect square on the left side: (x + 5)(x + 5) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + 5) equal to 3.464101615 and -3.464101615.Subproblem 1
x + 5 = 3.464101615 Simplifying x + 5 = 3.464101615 Reorder the terms: 5 + x = 3.464101615 Solving 5 + x = 3.464101615 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 = 3.464101615 + -5 Combine like terms: 5 + -5 = 0 0 + x = 3.464101615 + -5 x = 3.464101615 + -5 Combine like terms: 3.464101615 + -5 = -1.535898385 x = -1.535898385 Simplifying x = -1.535898385Subproblem 2
x + 5 = -3.464101615 Simplifying x + 5 = -3.464101615 Reorder the terms: 5 + x = -3.464101615 Solving 5 + x = -3.464101615 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 = -3.464101615 + -5 Combine like terms: 5 + -5 = 0 0 + x = -3.464101615 + -5 x = -3.464101615 + -5 Combine like terms: -3.464101615 + -5 = -8.464101615 x = -8.464101615 Simplifying x = -8.464101615Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.535898385, -8.464101615}
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