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Simplifying x2 + 10x + 4 = 0 Reorder the terms: 4 + 10x + x2 = 0 Solving 4 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 10x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 10x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 10x + x2 = 0 + -4 10x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 10x + x2 = -4 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 = -4 + 25 Reorder the terms: 25 + 10x + x2 = -4 + 25 Combine like terms: -4 + 25 = 21 25 + 10x + x2 = 21 Factor a perfect square on the left side: (x + 5)(x + 5) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (x + 5) equal to 4.582575695 and -4.582575695.Subproblem 1
x + 5 = 4.582575695 Simplifying x + 5 = 4.582575695 Reorder the terms: 5 + x = 4.582575695 Solving 5 + x = 4.582575695 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 = 4.582575695 + -5 Combine like terms: 5 + -5 = 0 0 + x = 4.582575695 + -5 x = 4.582575695 + -5 Combine like terms: 4.582575695 + -5 = -0.417424305 x = -0.417424305 Simplifying x = -0.417424305Subproblem 2
x + 5 = -4.582575695 Simplifying x + 5 = -4.582575695 Reorder the terms: 5 + x = -4.582575695 Solving 5 + x = -4.582575695 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 = -4.582575695 + -5 Combine like terms: 5 + -5 = 0 0 + x = -4.582575695 + -5 x = -4.582575695 + -5 Combine like terms: -4.582575695 + -5 = -9.582575695 x = -9.582575695 Simplifying x = -9.582575695Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.417424305, -9.582575695}
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