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Simplifying 6x2 + 21x + -1 = 0 Reorder the terms: -1 + 21x + 6x2 = 0 Solving -1 + 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'. -0.1666666667 + 3.5x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + 3.5x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + 3.5x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + 3.5x + x2 = 0 + 0.1666666667 3.5x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 3.5x + x2 = 0.1666666667 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 = 0.1666666667 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 0.1666666667 + 3.0625 Combine like terms: 0.1666666667 + 3.0625 = 3.2291666667 3.0625 + 3.5x + x2 = 3.2291666667 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 3.2291666667 Calculate the square root of the right side: 1.796988221 Break this problem into two subproblems by setting (x + 1.75) equal to 1.796988221 and -1.796988221.Subproblem 1
x + 1.75 = 1.796988221 Simplifying x + 1.75 = 1.796988221 Reorder the terms: 1.75 + x = 1.796988221 Solving 1.75 + x = 1.796988221 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 = 1.796988221 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 1.796988221 + -1.75 x = 1.796988221 + -1.75 Combine like terms: 1.796988221 + -1.75 = 0.046988221 x = 0.046988221 Simplifying x = 0.046988221Subproblem 2
x + 1.75 = -1.796988221 Simplifying x + 1.75 = -1.796988221 Reorder the terms: 1.75 + x = -1.796988221 Solving 1.75 + x = -1.796988221 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 = -1.796988221 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -1.796988221 + -1.75 x = -1.796988221 + -1.75 Combine like terms: -1.796988221 + -1.75 = -3.546988221 x = -3.546988221 Simplifying x = -3.546988221Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.046988221, -3.546988221}
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