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Simplifying 21x2 + -12x = -1 Reorder the terms: -12x + 21x2 = -1 Solving -12x + 21x2 = -1 Solving for variable 'x'. Reorder the terms: 1 + -12x + 21x2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + -12x + 21x2 = 0 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 = 0.03401360543 0.08163265305 + -0.5714285714x + x2 = 0.03401360543 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 0.03401360543 Calculate the square root of the right side: 0.184427778 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 0.184427778 and -0.184427778.Subproblem 1
x + -0.2857142857 = 0.184427778 Simplifying x + -0.2857142857 = 0.184427778 Reorder the terms: -0.2857142857 + x = 0.184427778 Solving -0.2857142857 + x = 0.184427778 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 = 0.184427778 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 0.184427778 + 0.2857142857 x = 0.184427778 + 0.2857142857 Combine like terms: 0.184427778 + 0.2857142857 = 0.4701420637 x = 0.4701420637 Simplifying x = 0.4701420637Subproblem 2
x + -0.2857142857 = -0.184427778 Simplifying x + -0.2857142857 = -0.184427778 Reorder the terms: -0.2857142857 + x = -0.184427778 Solving -0.2857142857 + x = -0.184427778 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 = -0.184427778 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -0.184427778 + 0.2857142857 x = -0.184427778 + 0.2857142857 Combine like terms: -0.184427778 + 0.2857142857 = 0.1012865077 x = 0.1012865077 Simplifying x = 0.1012865077Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4701420637, 0.1012865077}
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