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Simplifying 5x2 + 41x + 40 = 0 Reorder the terms: 40 + 41x + 5x2 = 0 Solving 40 + 41x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 8 + 8.2x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + 8.2x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + 8.2x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 8.2x + x2 = 0 + -8 8.2x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 8.2x + x2 = -8 The x term is 8.2x. Take half its coefficient (4.1). Square it (16.81) and add it to both sides. Add '16.81' to each side of the equation. 8.2x + 16.81 + x2 = -8 + 16.81 Reorder the terms: 16.81 + 8.2x + x2 = -8 + 16.81 Combine like terms: -8 + 16.81 = 8.81 16.81 + 8.2x + x2 = 8.81 Factor a perfect square on the left side: (x + 4.1)(x + 4.1) = 8.81 Calculate the square root of the right side: 2.968164416 Break this problem into two subproblems by setting (x + 4.1) equal to 2.968164416 and -2.968164416.Subproblem 1
x + 4.1 = 2.968164416 Simplifying x + 4.1 = 2.968164416 Reorder the terms: 4.1 + x = 2.968164416 Solving 4.1 + x = 2.968164416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.1' to each side of the equation. 4.1 + -4.1 + x = 2.968164416 + -4.1 Combine like terms: 4.1 + -4.1 = 0.0 0.0 + x = 2.968164416 + -4.1 x = 2.968164416 + -4.1 Combine like terms: 2.968164416 + -4.1 = -1.131835584 x = -1.131835584 Simplifying x = -1.131835584Subproblem 2
x + 4.1 = -2.968164416 Simplifying x + 4.1 = -2.968164416 Reorder the terms: 4.1 + x = -2.968164416 Solving 4.1 + x = -2.968164416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.1' to each side of the equation. 4.1 + -4.1 + x = -2.968164416 + -4.1 Combine like terms: 4.1 + -4.1 = 0.0 0.0 + x = -2.968164416 + -4.1 x = -2.968164416 + -4.1 Combine like terms: -2.968164416 + -4.1 = -7.068164416 x = -7.068164416 Simplifying x = -7.068164416Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.131835584, -7.068164416}
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