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Simplifying 21x2 + 3x + -2 = 0factored Reorder the terms: -2 + 3x + 21x2 = 0factored Anything times zero is zero. -2 + 3x + 21x2 = 0acdefort Solving -2 + 3x + 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 + 0.1428571429x + x2 = 0 Move the constant term to the right: Add '0.09523809524' to each side of the equation. -0.09523809524 + 0.1428571429x + 0.09523809524 + x2 = 0 + 0.09523809524 Reorder the terms: -0.09523809524 + 0.09523809524 + 0.1428571429x + x2 = 0 + 0.09523809524 Combine like terms: -0.09523809524 + 0.09523809524 = 0.00000000000 0.00000000000 + 0.1428571429x + x2 = 0 + 0.09523809524 0.1428571429x + x2 = 0 + 0.09523809524 Combine like terms: 0 + 0.09523809524 = 0.09523809524 0.1428571429x + x2 = 0.09523809524 The x term is 0.1428571429x. Take half its coefficient (0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. 0.1428571429x + 0.005102040819 + x2 = 0.09523809524 + 0.005102040819 Reorder the terms: 0.005102040819 + 0.1428571429x + x2 = 0.09523809524 + 0.005102040819 Combine like terms: 0.09523809524 + 0.005102040819 = 0.100340136059 0.005102040819 + 0.1428571429x + x2 = 0.100340136059 Factor a perfect square on the left side: (x + 0.07142857145)(x + 0.07142857145) = 0.100340136059 Calculate the square root of the right side: 0.316765112 Break this problem into two subproblems by setting (x + 0.07142857145) equal to 0.316765112 and -0.316765112.Subproblem 1
x + 0.07142857145 = 0.316765112 Simplifying x + 0.07142857145 = 0.316765112 Reorder the terms: 0.07142857145 + x = 0.316765112 Solving 0.07142857145 + x = 0.316765112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.07142857145' to each side of the equation. 0.07142857145 + -0.07142857145 + x = 0.316765112 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + x = 0.316765112 + -0.07142857145 x = 0.316765112 + -0.07142857145 Combine like terms: 0.316765112 + -0.07142857145 = 0.24533654055 x = 0.24533654055 Simplifying x = 0.24533654055Subproblem 2
x + 0.07142857145 = -0.316765112 Simplifying x + 0.07142857145 = -0.316765112 Reorder the terms: 0.07142857145 + x = -0.316765112 Solving 0.07142857145 + x = -0.316765112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.07142857145' to each side of the equation. 0.07142857145 + -0.07142857145 + x = -0.316765112 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + x = -0.316765112 + -0.07142857145 x = -0.316765112 + -0.07142857145 Combine like terms: -0.316765112 + -0.07142857145 = -0.38819368345 x = -0.38819368345 Simplifying x = -0.38819368345Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.24533654055, -0.38819368345}
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