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Simplifying 21x2 + 50x + -50 = 0 Reorder the terms: -50 + 50x + 21x2 = 0 Solving -50 + 50x + 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'. -2.380952381 + 2.380952381x + x2 = 0 Move the constant term to the right: Add '2.380952381' to each side of the equation. -2.380952381 + 2.380952381x + 2.380952381 + x2 = 0 + 2.380952381 Reorder the terms: -2.380952381 + 2.380952381 + 2.380952381x + x2 = 0 + 2.380952381 Combine like terms: -2.380952381 + 2.380952381 = 0.000000000 0.000000000 + 2.380952381x + x2 = 0 + 2.380952381 2.380952381x + x2 = 0 + 2.380952381 Combine like terms: 0 + 2.380952381 = 2.380952381 2.380952381x + x2 = 2.380952381 The x term is 2.380952381x. Take half its coefficient (1.190476191). Square it (1.417233561) and add it to both sides. Add '1.417233561' to each side of the equation. 2.380952381x + 1.417233561 + x2 = 2.380952381 + 1.417233561 Reorder the terms: 1.417233561 + 2.380952381x + x2 = 2.380952381 + 1.417233561 Combine like terms: 2.380952381 + 1.417233561 = 3.798185942 1.417233561 + 2.380952381x + x2 = 3.798185942 Factor a perfect square on the left side: (x + 1.190476191)(x + 1.190476191) = 3.798185942 Calculate the square root of the right side: 1.948893517 Break this problem into two subproblems by setting (x + 1.190476191) equal to 1.948893517 and -1.948893517.Subproblem 1
x + 1.190476191 = 1.948893517 Simplifying x + 1.190476191 = 1.948893517 Reorder the terms: 1.190476191 + x = 1.948893517 Solving 1.190476191 + x = 1.948893517 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.190476191' to each side of the equation. 1.190476191 + -1.190476191 + x = 1.948893517 + -1.190476191 Combine like terms: 1.190476191 + -1.190476191 = 0.000000000 0.000000000 + x = 1.948893517 + -1.190476191 x = 1.948893517 + -1.190476191 Combine like terms: 1.948893517 + -1.190476191 = 0.758417326 x = 0.758417326 Simplifying x = 0.758417326Subproblem 2
x + 1.190476191 = -1.948893517 Simplifying x + 1.190476191 = -1.948893517 Reorder the terms: 1.190476191 + x = -1.948893517 Solving 1.190476191 + x = -1.948893517 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.190476191' to each side of the equation. 1.190476191 + -1.190476191 + x = -1.948893517 + -1.190476191 Combine like terms: 1.190476191 + -1.190476191 = 0.000000000 0.000000000 + x = -1.948893517 + -1.190476191 x = -1.948893517 + -1.190476191 Combine like terms: -1.948893517 + -1.190476191 = -3.139369708 x = -3.139369708 Simplifying x = -3.139369708Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.758417326, -3.139369708}
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