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Simplifying 4x2 + 40x + 3 = 0 Reorder the terms: 3 + 40x + 4x2 = 0 Solving 3 + 40x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + 10x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 10x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 10x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 10x + x2 = 0 + -0.75 10x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 10x + x2 = -0.75 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -0.75 + 25 Reorder the terms: 25 + 10x + x2 = -0.75 + 25 Combine like terms: -0.75 + 25 = 24.25 25 + 10x + x2 = 24.25 Factor a perfect square on the left side: (x + 5)(x + 5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (x + 5) equal to 4.924428901 and -4.924428901.Subproblem 1
x + 5 = 4.924428901 Simplifying x + 5 = 4.924428901 Reorder the terms: 5 + x = 4.924428901 Solving 5 + x = 4.924428901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 4.924428901 + -5 Combine like terms: 5 + -5 = 0 0 + x = 4.924428901 + -5 x = 4.924428901 + -5 Combine like terms: 4.924428901 + -5 = -0.075571099 x = -0.075571099 Simplifying x = -0.075571099Subproblem 2
x + 5 = -4.924428901 Simplifying x + 5 = -4.924428901 Reorder the terms: 5 + x = -4.924428901 Solving 5 + x = -4.924428901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -4.924428901 + -5 Combine like terms: 5 + -5 = 0 0 + x = -4.924428901 + -5 x = -4.924428901 + -5 Combine like terms: -4.924428901 + -5 = -9.924428901 x = -9.924428901 Simplifying x = -9.924428901Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.075571099, -9.924428901}
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