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Simplifying 21x2 + -30x + 10 = 0 Reorder the terms: 10 + -30x + 21x2 = 0 Solving 10 + -30x + 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'. 0.4761904762 + -1.428571429x + x2 = 0 Move the constant term to the right: Add '-0.4761904762' to each side of the equation. 0.4761904762 + -1.428571429x + -0.4761904762 + x2 = 0 + -0.4761904762 Reorder the terms: 0.4761904762 + -0.4761904762 + -1.428571429x + x2 = 0 + -0.4761904762 Combine like terms: 0.4761904762 + -0.4761904762 = 0.0000000000 0.0000000000 + -1.428571429x + x2 = 0 + -0.4761904762 -1.428571429x + x2 = 0 + -0.4761904762 Combine like terms: 0 + -0.4761904762 = -0.4761904762 -1.428571429x + x2 = -0.4761904762 The x term is -1.428571429x. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429x + 0.5102040819 + x2 = -0.4761904762 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429x + x2 = -0.4761904762 + 0.5102040819 Combine like terms: -0.4761904762 + 0.5102040819 = 0.0340136057 0.5102040819 + -1.428571429x + x2 = 0.0340136057 Factor a perfect square on the left side: (x + -0.7142857145)(x + -0.7142857145) = 0.0340136057 Calculate the square root of the right side: 0.184427779 Break this problem into two subproblems by setting (x + -0.7142857145) equal to 0.184427779 and -0.184427779.Subproblem 1
x + -0.7142857145 = 0.184427779 Simplifying x + -0.7142857145 = 0.184427779 Reorder the terms: -0.7142857145 + x = 0.184427779 Solving -0.7142857145 + x = 0.184427779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = 0.184427779 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = 0.184427779 + 0.7142857145 x = 0.184427779 + 0.7142857145 Combine like terms: 0.184427779 + 0.7142857145 = 0.8987134935 x = 0.8987134935 Simplifying x = 0.8987134935Subproblem 2
x + -0.7142857145 = -0.184427779 Simplifying x + -0.7142857145 = -0.184427779 Reorder the terms: -0.7142857145 + x = -0.184427779 Solving -0.7142857145 + x = -0.184427779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = -0.184427779 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = -0.184427779 + 0.7142857145 x = -0.184427779 + 0.7142857145 Combine like terms: -0.184427779 + 0.7142857145 = 0.5298579355 x = 0.5298579355 Simplifying x = 0.5298579355Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8987134935, 0.5298579355}
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