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Simplifying 21x2 + -58x + 29 = 0 Reorder the terms: 29 + -58x + 21x2 = 0 Solving 29 + -58x + 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'. 1.380952381 + -2.761904762x + x2 = 0 Move the constant term to the right: Add '-1.380952381' to each side of the equation. 1.380952381 + -2.761904762x + -1.380952381 + x2 = 0 + -1.380952381 Reorder the terms: 1.380952381 + -1.380952381 + -2.761904762x + x2 = 0 + -1.380952381 Combine like terms: 1.380952381 + -1.380952381 = 0.000000000 0.000000000 + -2.761904762x + x2 = 0 + -1.380952381 -2.761904762x + x2 = 0 + -1.380952381 Combine like terms: 0 + -1.380952381 = -1.380952381 -2.761904762x + x2 = -1.380952381 The x term is -2.761904762x. Take half its coefficient (-1.380952381). Square it (1.907029479) and add it to both sides. Add '1.907029479' to each side of the equation. -2.761904762x + 1.907029479 + x2 = -1.380952381 + 1.907029479 Reorder the terms: 1.907029479 + -2.761904762x + x2 = -1.380952381 + 1.907029479 Combine like terms: -1.380952381 + 1.907029479 = 0.526077098 1.907029479 + -2.761904762x + x2 = 0.526077098 Factor a perfect square on the left side: (x + -1.380952381)(x + -1.380952381) = 0.526077098 Calculate the square root of the right side: 0.725311725 Break this problem into two subproblems by setting (x + -1.380952381) equal to 0.725311725 and -0.725311725.Subproblem 1
x + -1.380952381 = 0.725311725 Simplifying x + -1.380952381 = 0.725311725 Reorder the terms: -1.380952381 + x = 0.725311725 Solving -1.380952381 + x = 0.725311725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.380952381' to each side of the equation. -1.380952381 + 1.380952381 + x = 0.725311725 + 1.380952381 Combine like terms: -1.380952381 + 1.380952381 = 0.000000000 0.000000000 + x = 0.725311725 + 1.380952381 x = 0.725311725 + 1.380952381 Combine like terms: 0.725311725 + 1.380952381 = 2.106264106 x = 2.106264106 Simplifying x = 2.106264106Subproblem 2
x + -1.380952381 = -0.725311725 Simplifying x + -1.380952381 = -0.725311725 Reorder the terms: -1.380952381 + x = -0.725311725 Solving -1.380952381 + x = -0.725311725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.380952381' to each side of the equation. -1.380952381 + 1.380952381 + x = -0.725311725 + 1.380952381 Combine like terms: -1.380952381 + 1.380952381 = 0.000000000 0.000000000 + x = -0.725311725 + 1.380952381 x = -0.725311725 + 1.380952381 Combine like terms: -0.725311725 + 1.380952381 = 0.655640656 x = 0.655640656 Simplifying x = 0.655640656Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.106264106, 0.655640656}
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