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Simplifying 21x2 + -50x + 21 = 0 Reorder the terms: 21 + -50x + 21x2 = 0 Solving 21 + -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'. 1 + -2.380952381x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.380952381x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -2.380952381x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.380952381x + x2 = 0 + -1 -2.380952381x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.380952381x + x2 = -1 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 = -1 + 1.417233561 Reorder the terms: 1.417233561 + -2.380952381x + x2 = -1 + 1.417233561 Combine like terms: -1 + 1.417233561 = 0.417233561 1.417233561 + -2.380952381x + x2 = 0.417233561 Factor a perfect square on the left side: (x + -1.190476191)(x + -1.190476191) = 0.417233561 Calculate the square root of the right side: 0.64593619 Break this problem into two subproblems by setting (x + -1.190476191) equal to 0.64593619 and -0.64593619.Subproblem 1
x + -1.190476191 = 0.64593619 Simplifying x + -1.190476191 = 0.64593619 Reorder the terms: -1.190476191 + x = 0.64593619 Solving -1.190476191 + x = 0.64593619 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 = 0.64593619 + 1.190476191 Combine like terms: -1.190476191 + 1.190476191 = 0.000000000 0.000000000 + x = 0.64593619 + 1.190476191 x = 0.64593619 + 1.190476191 Combine like terms: 0.64593619 + 1.190476191 = 1.836412381 x = 1.836412381 Simplifying x = 1.836412381Subproblem 2
x + -1.190476191 = -0.64593619 Simplifying x + -1.190476191 = -0.64593619 Reorder the terms: -1.190476191 + x = -0.64593619 Solving -1.190476191 + x = -0.64593619 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 = -0.64593619 + 1.190476191 Combine like terms: -1.190476191 + 1.190476191 = 0.000000000 0.000000000 + x = -0.64593619 + 1.190476191 x = -0.64593619 + 1.190476191 Combine like terms: -0.64593619 + 1.190476191 = 0.544540001 x = 0.544540001 Simplifying x = 0.544540001Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.836412381, 0.544540001}
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