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Simplifying 21x2 + -50x + -613 = 0 Reorder the terms: -613 + -50x + 21x2 = 0 Solving -613 + -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'. -29.19047619 + -2.380952381x + x2 = 0 Move the constant term to the right: Add '29.19047619' to each side of the equation. -29.19047619 + -2.380952381x + 29.19047619 + x2 = 0 + 29.19047619 Reorder the terms: -29.19047619 + 29.19047619 + -2.380952381x + x2 = 0 + 29.19047619 Combine like terms: -29.19047619 + 29.19047619 = 0.00000000 0.00000000 + -2.380952381x + x2 = 0 + 29.19047619 -2.380952381x + x2 = 0 + 29.19047619 Combine like terms: 0 + 29.19047619 = 29.19047619 -2.380952381x + x2 = 29.19047619 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 = 29.19047619 + 1.417233561 Reorder the terms: 1.417233561 + -2.380952381x + x2 = 29.19047619 + 1.417233561 Combine like terms: 29.19047619 + 1.417233561 = 30.607709751 1.417233561 + -2.380952381x + x2 = 30.607709751 Factor a perfect square on the left side: (x + -1.190476191)(x + -1.190476191) = 30.607709751 Calculate the square root of the right side: 5.532423497 Break this problem into two subproblems by setting (x + -1.190476191) equal to 5.532423497 and -5.532423497.Subproblem 1
x + -1.190476191 = 5.532423497 Simplifying x + -1.190476191 = 5.532423497 Reorder the terms: -1.190476191 + x = 5.532423497 Solving -1.190476191 + x = 5.532423497 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 = 5.532423497 + 1.190476191 Combine like terms: -1.190476191 + 1.190476191 = 0.000000000 0.000000000 + x = 5.532423497 + 1.190476191 x = 5.532423497 + 1.190476191 Combine like terms: 5.532423497 + 1.190476191 = 6.722899688 x = 6.722899688 Simplifying x = 6.722899688Subproblem 2
x + -1.190476191 = -5.532423497 Simplifying x + -1.190476191 = -5.532423497 Reorder the terms: -1.190476191 + x = -5.532423497 Solving -1.190476191 + x = -5.532423497 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 = -5.532423497 + 1.190476191 Combine like terms: -1.190476191 + 1.190476191 = 0.000000000 0.000000000 + x = -5.532423497 + 1.190476191 x = -5.532423497 + 1.190476191 Combine like terms: -5.532423497 + 1.190476191 = -4.341947306 x = -4.341947306 Simplifying x = -4.341947306Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.722899688, -4.341947306}
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