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Simplifying x2 + 10x + 12 = 0 Reorder the terms: 12 + 10x + x2 = 0 Solving 12 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 10x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + 10x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 10x + x2 = 0 + -12 10x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 10x + x2 = -12 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 = -12 + 25 Reorder the terms: 25 + 10x + x2 = -12 + 25 Combine like terms: -12 + 25 = 13 25 + 10x + x2 = 13 Factor a perfect square on the left side: (x + 5)(x + 5) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x + 5) equal to 3.605551275 and -3.605551275.Subproblem 1
x + 5 = 3.605551275 Simplifying x + 5 = 3.605551275 Reorder the terms: 5 + x = 3.605551275 Solving 5 + x = 3.605551275 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 = 3.605551275 + -5 Combine like terms: 5 + -5 = 0 0 + x = 3.605551275 + -5 x = 3.605551275 + -5 Combine like terms: 3.605551275 + -5 = -1.394448725 x = -1.394448725 Simplifying x = -1.394448725Subproblem 2
x + 5 = -3.605551275 Simplifying x + 5 = -3.605551275 Reorder the terms: 5 + x = -3.605551275 Solving 5 + x = -3.605551275 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 = -3.605551275 + -5 Combine like terms: 5 + -5 = 0 0 + x = -3.605551275 + -5 x = -3.605551275 + -5 Combine like terms: -3.605551275 + -5 = -8.605551275 x = -8.605551275 Simplifying x = -8.605551275Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.394448725, -8.605551275}
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