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Simplifying 2x2 + 50x + 5 = 0 Reorder the terms: 5 + 50x + 2x2 = 0 Solving 5 + 50x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + 25x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 25x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 25x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 25x + x2 = 0 + -2.5 25x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 25x + x2 = -2.5 The x term is 25x. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25x + 156.25 + x2 = -2.5 + 156.25 Reorder the terms: 156.25 + 25x + x2 = -2.5 + 156.25 Combine like terms: -2.5 + 156.25 = 153.75 156.25 + 25x + x2 = 153.75 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 153.75 Calculate the square root of the right side: 12.399596768 Break this problem into two subproblems by setting (x + 12.5) equal to 12.399596768 and -12.399596768.Subproblem 1
x + 12.5 = 12.399596768 Simplifying x + 12.5 = 12.399596768 Reorder the terms: 12.5 + x = 12.399596768 Solving 12.5 + x = 12.399596768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 12.399596768 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 12.399596768 + -12.5 x = 12.399596768 + -12.5 Combine like terms: 12.399596768 + -12.5 = -0.100403232 x = -0.100403232 Simplifying x = -0.100403232Subproblem 2
x + 12.5 = -12.399596768 Simplifying x + 12.5 = -12.399596768 Reorder the terms: 12.5 + x = -12.399596768 Solving 12.5 + x = -12.399596768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -12.399596768 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -12.399596768 + -12.5 x = -12.399596768 + -12.5 Combine like terms: -12.399596768 + -12.5 = -24.899596768 x = -24.899596768 Simplifying x = -24.899596768Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.100403232, -24.899596768}
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