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Simplifying 2x2 + 24x + 1 = 0 Reorder the terms: 1 + 24x + 2x2 = 0 Solving 1 + 24x + 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'. 0.5 + 12x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 12x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 12x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 12x + x2 = 0 + -0.5 12x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 12x + x2 = -0.5 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = -0.5 + 36 Reorder the terms: 36 + 12x + x2 = -0.5 + 36 Combine like terms: -0.5 + 36 = 35.5 36 + 12x + x2 = 35.5 Factor a perfect square on the left side: (x + 6)(x + 6) = 35.5 Calculate the square root of the right side: 5.958187644 Break this problem into two subproblems by setting (x + 6) equal to 5.958187644 and -5.958187644.Subproblem 1
x + 6 = 5.958187644 Simplifying x + 6 = 5.958187644 Reorder the terms: 6 + x = 5.958187644 Solving 6 + x = 5.958187644 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 5.958187644 + -6 Combine like terms: 6 + -6 = 0 0 + x = 5.958187644 + -6 x = 5.958187644 + -6 Combine like terms: 5.958187644 + -6 = -0.041812356 x = -0.041812356 Simplifying x = -0.041812356Subproblem 2
x + 6 = -5.958187644 Simplifying x + 6 = -5.958187644 Reorder the terms: 6 + x = -5.958187644 Solving 6 + x = -5.958187644 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -5.958187644 + -6 Combine like terms: 6 + -6 = 0 0 + x = -5.958187644 + -6 x = -5.958187644 + -6 Combine like terms: -5.958187644 + -6 = -11.958187644 x = -11.958187644 Simplifying x = -11.958187644Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.041812356, -11.958187644}
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