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Simplifying 21x2 + -28x = 8 Reorder the terms: -28x + 21x2 = 8 Solving -28x + 21x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + -28x + 21x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -28x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -0.380952381 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '0.380952381' to each side of the equation. -0.380952381 + -1.333333333x + 0.380952381 + x2 = 0 + 0.380952381 Reorder the terms: -0.380952381 + 0.380952381 + -1.333333333x + x2 = 0 + 0.380952381 Combine like terms: -0.380952381 + 0.380952381 = 0.000000000 0.000000000 + -1.333333333x + x2 = 0 + 0.380952381 -1.333333333x + x2 = 0 + 0.380952381 Combine like terms: 0 + 0.380952381 = 0.380952381 -1.333333333x + x2 = 0.380952381 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = 0.380952381 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 0.380952381 + 0.4444444442 Combine like terms: 0.380952381 + 0.4444444442 = 0.8253968252 0.4444444442 + -1.333333333x + x2 = 0.8253968252 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 0.8253968252 Calculate the square root of the right side: 0.908513525 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 0.908513525 and -0.908513525.Subproblem 1
x + -0.6666666665 = 0.908513525 Simplifying x + -0.6666666665 = 0.908513525 Reorder the terms: -0.6666666665 + x = 0.908513525 Solving -0.6666666665 + x = 0.908513525 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 0.908513525 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 0.908513525 + 0.6666666665 x = 0.908513525 + 0.6666666665 Combine like terms: 0.908513525 + 0.6666666665 = 1.5751801915 x = 1.5751801915 Simplifying x = 1.5751801915Subproblem 2
x + -0.6666666665 = -0.908513525 Simplifying x + -0.6666666665 = -0.908513525 Reorder the terms: -0.6666666665 + x = -0.908513525 Solving -0.6666666665 + x = -0.908513525 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -0.908513525 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -0.908513525 + 0.6666666665 x = -0.908513525 + 0.6666666665 Combine like terms: -0.908513525 + 0.6666666665 = -0.2418468585 x = -0.2418468585 Simplifying x = -0.2418468585Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5751801915, -0.2418468585}
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