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Simplifying 2x2 + 6x + -40 = x Reorder the terms: -40 + 6x + 2x2 = x Solving -40 + 6x + 2x2 = x Solving for variable 'x'. Reorder the terms: -40 + 6x + -1x + 2x2 = x + -1x Combine like terms: 6x + -1x = 5x -40 + 5x + 2x2 = x + -1x Combine like terms: x + -1x = 0 -40 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -20 + 2.5x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 2.5x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 2.5x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 2.5x + x2 = 0 + 20 2.5x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 2.5x + x2 = 20 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 20 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 20 + 1.5625 Combine like terms: 20 + 1.5625 = 21.5625 1.5625 + 2.5x + x2 = 21.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 21.5625 Calculate the square root of the right side: 4.643543905 Break this problem into two subproblems by setting (x + 1.25) equal to 4.643543905 and -4.643543905.Subproblem 1
x + 1.25 = 4.643543905 Simplifying x + 1.25 = 4.643543905 Reorder the terms: 1.25 + x = 4.643543905 Solving 1.25 + x = 4.643543905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 4.643543905 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 4.643543905 + -1.25 x = 4.643543905 + -1.25 Combine like terms: 4.643543905 + -1.25 = 3.393543905 x = 3.393543905 Simplifying x = 3.393543905Subproblem 2
x + 1.25 = -4.643543905 Simplifying x + 1.25 = -4.643543905 Reorder the terms: 1.25 + x = -4.643543905 Solving 1.25 + x = -4.643543905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -4.643543905 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -4.643543905 + -1.25 x = -4.643543905 + -1.25 Combine like terms: -4.643543905 + -1.25 = -5.893543905 x = -5.893543905 Simplifying x = -5.893543905Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.393543905, -5.893543905}
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