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Simplifying 21x2 = 35x + -8 Reorder the terms: 21x2 = -8 + 35x Solving 21x2 = -8 + 35x Solving for variable 'x'. Reorder the terms: 8 + -35x + 21x2 = -8 + 35x + 8 + -35x Reorder the terms: 8 + -35x + 21x2 = -8 + 8 + 35x + -35x Combine like terms: -8 + 8 = 0 8 + -35x + 21x2 = 0 + 35x + -35x 8 + -35x + 21x2 = 35x + -35x Combine like terms: 35x + -35x = 0 8 + -35x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 0.380952381 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '-0.380952381' to each side of the equation. 0.380952381 + -1.666666667x + -0.380952381 + x2 = 0 + -0.380952381 Reorder the terms: 0.380952381 + -0.380952381 + -1.666666667x + x2 = 0 + -0.380952381 Combine like terms: 0.380952381 + -0.380952381 = 0.000000000 0.000000000 + -1.666666667x + x2 = 0 + -0.380952381 -1.666666667x + x2 = 0 + -0.380952381 Combine like terms: 0 + -0.380952381 = -0.380952381 -1.666666667x + x2 = -0.380952381 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = -0.380952381 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = -0.380952381 + 0.6944444447 Combine like terms: -0.380952381 + 0.6944444447 = 0.3134920637 0.6944444447 + -1.666666667x + x2 = 0.3134920637 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 0.3134920637 Calculate the square root of the right side: 0.55990362 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 0.55990362 and -0.55990362.Subproblem 1
x + -0.8333333335 = 0.55990362 Simplifying x + -0.8333333335 = 0.55990362 Reorder the terms: -0.8333333335 + x = 0.55990362 Solving -0.8333333335 + x = 0.55990362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 0.55990362 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 0.55990362 + 0.8333333335 x = 0.55990362 + 0.8333333335 Combine like terms: 0.55990362 + 0.8333333335 = 1.3932369535 x = 1.3932369535 Simplifying x = 1.3932369535Subproblem 2
x + -0.8333333335 = -0.55990362 Simplifying x + -0.8333333335 = -0.55990362 Reorder the terms: -0.8333333335 + x = -0.55990362 Solving -0.8333333335 + x = -0.55990362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -0.55990362 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -0.55990362 + 0.8333333335 x = -0.55990362 + 0.8333333335 Combine like terms: -0.55990362 + 0.8333333335 = 0.2734297135 x = 0.2734297135 Simplifying x = 0.2734297135Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3932369535, 0.2734297135}
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