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Simplifying 25x2 + 40x + 4 = 0 Reorder the terms: 4 + 40x + 25x2 = 0 Solving 4 + 40x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.16 + 1.6x + x2 = 0 Move the constant term to the right: Add '-0.16' to each side of the equation. 0.16 + 1.6x + -0.16 + x2 = 0 + -0.16 Reorder the terms: 0.16 + -0.16 + 1.6x + x2 = 0 + -0.16 Combine like terms: 0.16 + -0.16 = 0.00 0.00 + 1.6x + x2 = 0 + -0.16 1.6x + x2 = 0 + -0.16 Combine like terms: 0 + -0.16 = -0.16 1.6x + x2 = -0.16 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = -0.16 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = -0.16 + 0.64 Combine like terms: -0.16 + 0.64 = 0.48 0.64 + 1.6x + x2 = 0.48 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 0.48 Calculate the square root of the right side: 0.692820323 Break this problem into two subproblems by setting (x + 0.8) equal to 0.692820323 and -0.692820323.Subproblem 1
x + 0.8 = 0.692820323 Simplifying x + 0.8 = 0.692820323 Reorder the terms: 0.8 + x = 0.692820323 Solving 0.8 + x = 0.692820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 0.692820323 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 0.692820323 + -0.8 x = 0.692820323 + -0.8 Combine like terms: 0.692820323 + -0.8 = -0.107179677 x = -0.107179677 Simplifying x = -0.107179677Subproblem 2
x + 0.8 = -0.692820323 Simplifying x + 0.8 = -0.692820323 Reorder the terms: 0.8 + x = -0.692820323 Solving 0.8 + x = -0.692820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -0.692820323 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -0.692820323 + -0.8 x = -0.692820323 + -0.8 Combine like terms: -0.692820323 + -0.8 = -1.492820323 x = -1.492820323 Simplifying x = -1.492820323Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.107179677, -1.492820323}
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