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Simplifying 21x2 + -2x + -1 = 0 Reorder the terms: -1 + -2x + 21x2 = 0 Solving -1 + -2x + 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 + -0.09523809524x + x2 = 0 Move the constant term to the right: Add '0.04761904762' to each side of the equation. -0.04761904762 + -0.09523809524x + 0.04761904762 + x2 = 0 + 0.04761904762 Reorder the terms: -0.04761904762 + 0.04761904762 + -0.09523809524x + x2 = 0 + 0.04761904762 Combine like terms: -0.04761904762 + 0.04761904762 = 0.00000000000 0.00000000000 + -0.09523809524x + x2 = 0 + 0.04761904762 -0.09523809524x + x2 = 0 + 0.04761904762 Combine like terms: 0 + 0.04761904762 = 0.04761904762 -0.09523809524x + x2 = 0.04761904762 The x term is -0.09523809524x. Take half its coefficient (-0.04761904762). Square it (0.002267573696) and add it to both sides. Add '0.002267573696' to each side of the equation. -0.09523809524x + 0.002267573696 + x2 = 0.04761904762 + 0.002267573696 Reorder the terms: 0.002267573696 + -0.09523809524x + x2 = 0.04761904762 + 0.002267573696 Combine like terms: 0.04761904762 + 0.002267573696 = 0.049886621316 0.002267573696 + -0.09523809524x + x2 = 0.049886621316 Factor a perfect square on the left side: (x + -0.04761904762)(x + -0.04761904762) = 0.049886621316 Calculate the square root of the right side: 0.223353131 Break this problem into two subproblems by setting (x + -0.04761904762) equal to 0.223353131 and -0.223353131.Subproblem 1
x + -0.04761904762 = 0.223353131 Simplifying x + -0.04761904762 = 0.223353131 Reorder the terms: -0.04761904762 + x = 0.223353131 Solving -0.04761904762 + x = 0.223353131 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04761904762' to each side of the equation. -0.04761904762 + 0.04761904762 + x = 0.223353131 + 0.04761904762 Combine like terms: -0.04761904762 + 0.04761904762 = 0.00000000000 0.00000000000 + x = 0.223353131 + 0.04761904762 x = 0.223353131 + 0.04761904762 Combine like terms: 0.223353131 + 0.04761904762 = 0.27097217862 x = 0.27097217862 Simplifying x = 0.27097217862Subproblem 2
x + -0.04761904762 = -0.223353131 Simplifying x + -0.04761904762 = -0.223353131 Reorder the terms: -0.04761904762 + x = -0.223353131 Solving -0.04761904762 + x = -0.223353131 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04761904762' to each side of the equation. -0.04761904762 + 0.04761904762 + x = -0.223353131 + 0.04761904762 Combine like terms: -0.04761904762 + 0.04761904762 = 0.00000000000 0.00000000000 + x = -0.223353131 + 0.04761904762 x = -0.223353131 + 0.04761904762 Combine like terms: -0.223353131 + 0.04761904762 = -0.17573408338 x = -0.17573408338 Simplifying x = -0.17573408338Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.27097217862, -0.17573408338}
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