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Simplifying 21x2 + 12x + -1 = 0 Reorder the terms: -1 + 12x + 21x2 = 0 Solving -1 + 12x + 21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -0.04761904762 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '0.04761904762' to each side of the equation. -0.04761904762 + 0.5714285714x + 0.04761904762 + x2 = 0 + 0.04761904762 Reorder the terms: -0.04761904762 + 0.04761904762 + 0.5714285714x + x2 = 0 + 0.04761904762 Combine like terms: -0.04761904762 + 0.04761904762 = 0.00000000000 0.00000000000 + 0.5714285714x + x2 = 0 + 0.04761904762 0.5714285714x + x2 = 0 + 0.04761904762 Combine like terms: 0 + 0.04761904762 = 0.04761904762 0.5714285714x + x2 = 0.04761904762 The x term is 0.5714285714x. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714x + 0.08163265305 + x2 = 0.04761904762 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = 0.04761904762 + 0.08163265305 Combine like terms: 0.04761904762 + 0.08163265305 = 0.12925170067 0.08163265305 + 0.5714285714x + x2 = 0.12925170067 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = 0.12925170067 Calculate the square root of the right side: 0.359515925 Break this problem into two subproblems by setting (x + 0.2857142857) equal to 0.359515925 and -0.359515925.Subproblem 1
x + 0.2857142857 = 0.359515925 Simplifying x + 0.2857142857 = 0.359515925 Reorder the terms: 0.2857142857 + x = 0.359515925 Solving 0.2857142857 + x = 0.359515925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = 0.359515925 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = 0.359515925 + -0.2857142857 x = 0.359515925 + -0.2857142857 Combine like terms: 0.359515925 + -0.2857142857 = 0.0738016393 x = 0.0738016393 Simplifying x = 0.0738016393Subproblem 2
x + 0.2857142857 = -0.359515925 Simplifying x + 0.2857142857 = -0.359515925 Reorder the terms: 0.2857142857 + x = -0.359515925 Solving 0.2857142857 + x = -0.359515925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = -0.359515925 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = -0.359515925 + -0.2857142857 x = -0.359515925 + -0.2857142857 Combine like terms: -0.359515925 + -0.2857142857 = -0.6452302107 x = -0.6452302107 Simplifying x = -0.6452302107Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0738016393, -0.6452302107}
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