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Simplifying 5x2 + 41x + 4 = 0 Reorder the terms: 4 + 41x + 5x2 = 0 Solving 4 + 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'. 0.8 + 8.2x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + 8.2x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + 8.2x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + 8.2x + x2 = 0 + -0.8 8.2x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 8.2x + x2 = -0.8 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 = -0.8 + 16.81 Reorder the terms: 16.81 + 8.2x + x2 = -0.8 + 16.81 Combine like terms: -0.8 + 16.81 = 16.01 16.81 + 8.2x + x2 = 16.01 Factor a perfect square on the left side: (x + 4.1)(x + 4.1) = 16.01 Calculate the square root of the right side: 4.001249805 Break this problem into two subproblems by setting (x + 4.1) equal to 4.001249805 and -4.001249805.Subproblem 1
x + 4.1 = 4.001249805 Simplifying x + 4.1 = 4.001249805 Reorder the terms: 4.1 + x = 4.001249805 Solving 4.1 + x = 4.001249805 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 = 4.001249805 + -4.1 Combine like terms: 4.1 + -4.1 = 0.0 0.0 + x = 4.001249805 + -4.1 x = 4.001249805 + -4.1 Combine like terms: 4.001249805 + -4.1 = -0.098750195 x = -0.098750195 Simplifying x = -0.098750195Subproblem 2
x + 4.1 = -4.001249805 Simplifying x + 4.1 = -4.001249805 Reorder the terms: 4.1 + x = -4.001249805 Solving 4.1 + x = -4.001249805 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 = -4.001249805 + -4.1 Combine like terms: 4.1 + -4.1 = 0.0 0.0 + x = -4.001249805 + -4.1 x = -4.001249805 + -4.1 Combine like terms: -4.001249805 + -4.1 = -8.101249805 x = -8.101249805 Simplifying x = -8.101249805Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.098750195, -8.101249805}
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