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Simplifying x2 + 20x + 42 = 0 Reorder the terms: 42 + 20x + x2 = 0 Solving 42 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-42' to each side of the equation. 42 + 20x + -42 + x2 = 0 + -42 Reorder the terms: 42 + -42 + 20x + x2 = 0 + -42 Combine like terms: 42 + -42 = 0 0 + 20x + x2 = 0 + -42 20x + x2 = 0 + -42 Combine like terms: 0 + -42 = -42 20x + x2 = -42 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = -42 + 100 Reorder the terms: 100 + 20x + x2 = -42 + 100 Combine like terms: -42 + 100 = 58 100 + 20x + x2 = 58 Factor a perfect square on the left side: (x + 10)(x + 10) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (x + 10) equal to 7.615773106 and -7.615773106.Subproblem 1
x + 10 = 7.615773106 Simplifying x + 10 = 7.615773106 Reorder the terms: 10 + x = 7.615773106 Solving 10 + x = 7.615773106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 7.615773106 + -10 Combine like terms: 10 + -10 = 0 0 + x = 7.615773106 + -10 x = 7.615773106 + -10 Combine like terms: 7.615773106 + -10 = -2.384226894 x = -2.384226894 Simplifying x = -2.384226894Subproblem 2
x + 10 = -7.615773106 Simplifying x + 10 = -7.615773106 Reorder the terms: 10 + x = -7.615773106 Solving 10 + x = -7.615773106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -7.615773106 + -10 Combine like terms: 10 + -10 = 0 0 + x = -7.615773106 + -10 x = -7.615773106 + -10 Combine like terms: -7.615773106 + -10 = -17.615773106 x = -17.615773106 Simplifying x = -17.615773106Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.384226894, -17.615773106}
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