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Simplifying 6x2 + 15x + 1 = 0 Reorder the terms: 1 + 15x + 6x2 = 0 Solving 1 + 15x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.1666666667 + 2.5x + x2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + 2.5x + -0.1666666667 + x2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + 2.5x + x2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + 2.5x + x2 = 0 + -0.1666666667 2.5x + x2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 2.5x + x2 = -0.1666666667 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = -0.1666666667 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = -0.1666666667 + 1.5625 Combine like terms: -0.1666666667 + 1.5625 = 1.3958333333 1.5625 + 2.5x + x2 = 1.3958333333 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 1.3958333333 Calculate the square root of the right side: 1.181453907 Break this problem into two subproblems by setting (x + 1.25) equal to 1.181453907 and -1.181453907.Subproblem 1
x + 1.25 = 1.181453907 Simplifying x + 1.25 = 1.181453907 Reorder the terms: 1.25 + x = 1.181453907 Solving 1.25 + x = 1.181453907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 1.181453907 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.181453907 + -1.25 x = 1.181453907 + -1.25 Combine like terms: 1.181453907 + -1.25 = -0.068546093 x = -0.068546093 Simplifying x = -0.068546093Subproblem 2
x + 1.25 = -1.181453907 Simplifying x + 1.25 = -1.181453907 Reorder the terms: 1.25 + x = -1.181453907 Solving 1.25 + x = -1.181453907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -1.181453907 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.181453907 + -1.25 x = -1.181453907 + -1.25 Combine like terms: -1.181453907 + -1.25 = -2.431453907 x = -2.431453907 Simplifying x = -2.431453907Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.068546093, -2.431453907}
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