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Simplifying 2x2 + 13x + -21 = 1 Reorder the terms: -21 + 13x + 2x2 = 1 Solving -21 + 13x + 2x2 = 1 Solving for variable 'x'. Reorder the terms: -21 + -1 + 13x + 2x2 = 1 + -1 Combine like terms: -21 + -1 = -22 -22 + 13x + 2x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -22 + 13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -11 + 6.5x + x2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + 6.5x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 6.5x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 6.5x + x2 = 0 + 11 6.5x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 6.5x + x2 = 11 The x term is 6.5x. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5x + 10.5625 + x2 = 11 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = 11 + 10.5625 Combine like terms: 11 + 10.5625 = 21.5625 10.5625 + 6.5x + x2 = 21.5625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 21.5625 Calculate the square root of the right side: 4.643543905 Break this problem into two subproblems by setting (x + 3.25) equal to 4.643543905 and -4.643543905.Subproblem 1
x + 3.25 = 4.643543905 Simplifying x + 3.25 = 4.643543905 Reorder the terms: 3.25 + x = 4.643543905 Solving 3.25 + x = 4.643543905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 4.643543905 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 4.643543905 + -3.25 x = 4.643543905 + -3.25 Combine like terms: 4.643543905 + -3.25 = 1.393543905 x = 1.393543905 Simplifying x = 1.393543905Subproblem 2
x + 3.25 = -4.643543905 Simplifying x + 3.25 = -4.643543905 Reorder the terms: 3.25 + x = -4.643543905 Solving 3.25 + x = -4.643543905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -4.643543905 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -4.643543905 + -3.25 x = -4.643543905 + -3.25 Combine like terms: -4.643543905 + -3.25 = -7.893543905 x = -7.893543905 Simplifying x = -7.893543905Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.393543905, -7.893543905}
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