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Simplifying 6x2 + 21x + 13 = 0 Reorder the terms: 13 + 21x + 6x2 = 0 Solving 13 + 21x + 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'. 2.166666667 + 3.5x + x2 = 0 Move the constant term to the right: Add '-2.166666667' to each side of the equation. 2.166666667 + 3.5x + -2.166666667 + x2 = 0 + -2.166666667 Reorder the terms: 2.166666667 + -2.166666667 + 3.5x + x2 = 0 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + 3.5x + x2 = 0 + -2.166666667 3.5x + x2 = 0 + -2.166666667 Combine like terms: 0 + -2.166666667 = -2.166666667 3.5x + x2 = -2.166666667 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = -2.166666667 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = -2.166666667 + 3.0625 Combine like terms: -2.166666667 + 3.0625 = 0.895833333 3.0625 + 3.5x + x2 = 0.895833333 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 0.895833333 Calculate the square root of the right side: 0.946484724 Break this problem into two subproblems by setting (x + 1.75) equal to 0.946484724 and -0.946484724.Subproblem 1
x + 1.75 = 0.946484724 Simplifying x + 1.75 = 0.946484724 Reorder the terms: 1.75 + x = 0.946484724 Solving 1.75 + x = 0.946484724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 0.946484724 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 0.946484724 + -1.75 x = 0.946484724 + -1.75 Combine like terms: 0.946484724 + -1.75 = -0.803515276 x = -0.803515276 Simplifying x = -0.803515276Subproblem 2
x + 1.75 = -0.946484724 Simplifying x + 1.75 = -0.946484724 Reorder the terms: 1.75 + x = -0.946484724 Solving 1.75 + x = -0.946484724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -0.946484724 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -0.946484724 + -1.75 x = -0.946484724 + -1.75 Combine like terms: -0.946484724 + -1.75 = -2.696484724 x = -2.696484724 Simplifying x = -2.696484724Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.803515276, -2.696484724}
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