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Simplifying 5x2 + 40x + 4 = 0 Reorder the terms: 4 + 40x + 5x2 = 0 Solving 4 + 40x + 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'. 0.8 + 8x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + 8x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + 8x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + 8x + x2 = 0 + -0.8 8x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 8x + x2 = -0.8 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -0.8 + 16 Reorder the terms: 16 + 8x + x2 = -0.8 + 16 Combine like terms: -0.8 + 16 = 15.2 16 + 8x + x2 = 15.2 Factor a perfect square on the left side: (x + 4)(x + 4) = 15.2 Calculate the square root of the right side: 3.898717738 Break this problem into two subproblems by setting (x + 4) equal to 3.898717738 and -3.898717738.Subproblem 1
x + 4 = 3.898717738 Simplifying x + 4 = 3.898717738 Reorder the terms: 4 + x = 3.898717738 Solving 4 + x = 3.898717738 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 3.898717738 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.898717738 + -4 x = 3.898717738 + -4 Combine like terms: 3.898717738 + -4 = -0.101282262 x = -0.101282262 Simplifying x = -0.101282262Subproblem 2
x + 4 = -3.898717738 Simplifying x + 4 = -3.898717738 Reorder the terms: 4 + x = -3.898717738 Solving 4 + x = -3.898717738 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -3.898717738 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.898717738 + -4 x = -3.898717738 + -4 Combine like terms: -3.898717738 + -4 = -7.898717738 x = -7.898717738 Simplifying x = -7.898717738Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.101282262, -7.898717738}
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