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Simplifying 21x2 + -10x + -2 = 0 Reorder the terms: -2 + -10x + 21x2 = 0 Solving -2 + -10x + 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'. -0.09523809524 + -0.4761904762x + x2 = 0 Move the constant term to the right: Add '0.09523809524' to each side of the equation. -0.09523809524 + -0.4761904762x + 0.09523809524 + x2 = 0 + 0.09523809524 Reorder the terms: -0.09523809524 + 0.09523809524 + -0.4761904762x + x2 = 0 + 0.09523809524 Combine like terms: -0.09523809524 + 0.09523809524 = 0.00000000000 0.00000000000 + -0.4761904762x + x2 = 0 + 0.09523809524 -0.4761904762x + x2 = 0 + 0.09523809524 Combine like terms: 0 + 0.09523809524 = 0.09523809524 -0.4761904762x + x2 = 0.09523809524 The x term is -0.4761904762x. Take half its coefficient (-0.2380952381). Square it (0.05668934241) and add it to both sides. Add '0.05668934241' to each side of the equation. -0.4761904762x + 0.05668934241 + x2 = 0.09523809524 + 0.05668934241 Reorder the terms: 0.05668934241 + -0.4761904762x + x2 = 0.09523809524 + 0.05668934241 Combine like terms: 0.09523809524 + 0.05668934241 = 0.15192743765 0.05668934241 + -0.4761904762x + x2 = 0.15192743765 Factor a perfect square on the left side: (x + -0.2380952381)(x + -0.2380952381) = 0.15192743765 Calculate the square root of the right side: 0.389778703 Break this problem into two subproblems by setting (x + -0.2380952381) equal to 0.389778703 and -0.389778703.Subproblem 1
x + -0.2380952381 = 0.389778703 Simplifying x + -0.2380952381 = 0.389778703 Reorder the terms: -0.2380952381 + x = 0.389778703 Solving -0.2380952381 + x = 0.389778703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2380952381' to each side of the equation. -0.2380952381 + 0.2380952381 + x = 0.389778703 + 0.2380952381 Combine like terms: -0.2380952381 + 0.2380952381 = 0.0000000000 0.0000000000 + x = 0.389778703 + 0.2380952381 x = 0.389778703 + 0.2380952381 Combine like terms: 0.389778703 + 0.2380952381 = 0.6278739411 x = 0.6278739411 Simplifying x = 0.6278739411Subproblem 2
x + -0.2380952381 = -0.389778703 Simplifying x + -0.2380952381 = -0.389778703 Reorder the terms: -0.2380952381 + x = -0.389778703 Solving -0.2380952381 + x = -0.389778703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2380952381' to each side of the equation. -0.2380952381 + 0.2380952381 + x = -0.389778703 + 0.2380952381 Combine like terms: -0.2380952381 + 0.2380952381 = 0.0000000000 0.0000000000 + x = -0.389778703 + 0.2380952381 x = -0.389778703 + 0.2380952381 Combine like terms: -0.389778703 + 0.2380952381 = -0.1516834649 x = -0.1516834649 Simplifying x = -0.1516834649Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6278739411, -0.1516834649}
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