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Simplifying 2x2 + 2x + -40 = 9 Reorder the terms: -40 + 2x + 2x2 = 9 Solving -40 + 2x + 2x2 = 9 Solving for variable 'x'. Reorder the terms: -40 + -9 + 2x + 2x2 = 9 + -9 Combine like terms: -40 + -9 = -49 -49 + 2x + 2x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -49 + 2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -24.5 + x + x2 = 0 Move the constant term to the right: Add '24.5' to each side of the equation. -24.5 + x + 24.5 + x2 = 0 + 24.5 Reorder the terms: -24.5 + 24.5 + x + x2 = 0 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x + x2 = 0 + 24.5 x + x2 = 0 + 24.5 Combine like terms: 0 + 24.5 = 24.5 x + x2 = 24.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 24.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 24.5 + 0.25 Combine like terms: 24.5 + 0.25 = 24.75 1.25 + x2 = 24.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 24.75 Calculate the square root of the right side: 4.974937186 Break this problem into two subproblems by setting (x + 0.5) equal to 4.974937186 and -4.974937186.Subproblem 1
x + 0.5 = 4.974937186 Simplifying x + 0.5 = 4.974937186 Reorder the terms: 0.5 + x = 4.974937186 Solving 0.5 + x = 4.974937186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4.974937186 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.974937186 + -0.5 x = 4.974937186 + -0.5 Combine like terms: 4.974937186 + -0.5 = 4.474937186 x = 4.474937186 Simplifying x = 4.474937186Subproblem 2
x + 0.5 = -4.974937186 Simplifying x + 0.5 = -4.974937186 Reorder the terms: 0.5 + x = -4.974937186 Solving 0.5 + x = -4.974937186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4.974937186 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.974937186 + -0.5 x = -4.974937186 + -0.5 Combine like terms: -4.974937186 + -0.5 = -5.474937186 x = -5.474937186 Simplifying x = -5.474937186Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.474937186, -5.474937186}
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