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Simplifying -2x2 + 5x + 40 = 0 Reorder the terms: 40 + 5x + -2x2 = 0 Solving 40 + 5x + -2x2 = 0 Solving for variable 'x'. 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 = 5.893543905 x = 5.893543905 Simplifying x = 5.893543905Subproblem 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 = -3.393543905 x = -3.393543905 Simplifying x = -3.393543905Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.893543905, -3.393543905}
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