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Simplifying 3x2 + 15x + 1 = 0 Reorder the terms: 1 + 15x + 3x2 = 0 Solving 1 + 15x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + 5x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 5x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 5x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 5x + x2 = 0 + -0.3333333333 5x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 5x + x2 = -0.3333333333 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -0.3333333333 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -0.3333333333 + 6.25 Combine like terms: -0.3333333333 + 6.25 = 5.9166666667 6.25 + 5x + x2 = 5.9166666667 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 5.9166666667 Calculate the square root of the right side: 2.43241992 Break this problem into two subproblems by setting (x + 2.5) equal to 2.43241992 and -2.43241992.Subproblem 1
x + 2.5 = 2.43241992 Simplifying x + 2.5 = 2.43241992 Reorder the terms: 2.5 + x = 2.43241992 Solving 2.5 + x = 2.43241992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.43241992 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.43241992 + -2.5 x = 2.43241992 + -2.5 Combine like terms: 2.43241992 + -2.5 = -0.06758008 x = -0.06758008 Simplifying x = -0.06758008Subproblem 2
x + 2.5 = -2.43241992 Simplifying x + 2.5 = -2.43241992 Reorder the terms: 2.5 + x = -2.43241992 Solving 2.5 + x = -2.43241992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.43241992 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.43241992 + -2.5 x = -2.43241992 + -2.5 Combine like terms: -2.43241992 + -2.5 = -4.93241992 x = -4.93241992 Simplifying x = -4.93241992Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.06758008, -4.93241992}
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