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Simplifying 21x2 + 5x + -7 = 0 Reorder the terms: -7 + 5x + 21x2 = 0 Solving -7 + 5x + 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'. -0.3333333333 + 0.2380952381x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 0.2380952381x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 0.2380952381x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 0.2380952381x + x2 = 0 + 0.3333333333 0.2380952381x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 0.2380952381x + x2 = 0.3333333333 The x term is 0.2380952381x. Take half its coefficient (0.1190476191). Square it (0.01417233561) and add it to both sides. Add '0.01417233561' to each side of the equation. 0.2380952381x + 0.01417233561 + x2 = 0.3333333333 + 0.01417233561 Reorder the terms: 0.01417233561 + 0.2380952381x + x2 = 0.3333333333 + 0.01417233561 Combine like terms: 0.3333333333 + 0.01417233561 = 0.34750566891 0.01417233561 + 0.2380952381x + x2 = 0.34750566891 Factor a perfect square on the left side: (x + 0.1190476191)(x + 0.1190476191) = 0.34750566891 Calculate the square root of the right side: 0.589496114 Break this problem into two subproblems by setting (x + 0.1190476191) equal to 0.589496114 and -0.589496114.Subproblem 1
x + 0.1190476191 = 0.589496114 Simplifying x + 0.1190476191 = 0.589496114 Reorder the terms: 0.1190476191 + x = 0.589496114 Solving 0.1190476191 + x = 0.589496114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1190476191' to each side of the equation. 0.1190476191 + -0.1190476191 + x = 0.589496114 + -0.1190476191 Combine like terms: 0.1190476191 + -0.1190476191 = 0.0000000000 0.0000000000 + x = 0.589496114 + -0.1190476191 x = 0.589496114 + -0.1190476191 Combine like terms: 0.589496114 + -0.1190476191 = 0.4704484949 x = 0.4704484949 Simplifying x = 0.4704484949Subproblem 2
x + 0.1190476191 = -0.589496114 Simplifying x + 0.1190476191 = -0.589496114 Reorder the terms: 0.1190476191 + x = -0.589496114 Solving 0.1190476191 + x = -0.589496114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1190476191' to each side of the equation. 0.1190476191 + -0.1190476191 + x = -0.589496114 + -0.1190476191 Combine like terms: 0.1190476191 + -0.1190476191 = 0.0000000000 0.0000000000 + x = -0.589496114 + -0.1190476191 x = -0.589496114 + -0.1190476191 Combine like terms: -0.589496114 + -0.1190476191 = -0.7085437331 x = -0.7085437331 Simplifying x = -0.7085437331Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4704484949, -0.7085437331}
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