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Simplifying 5x2 + 14.1x + 5 = 0 Reorder the terms: 5 + 14.1x + 5x2 = 0 Solving 5 + 14.1x + 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'. 1 + 2.82x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 2.82x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 2.82x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2.82x + x2 = 0 + -1 2.82x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 2.82x + x2 = -1 The x term is 2.82x. Take half its coefficient (1.41). Square it (1.9881) and add it to both sides. Add '1.9881' to each side of the equation. 2.82x + 1.9881 + x2 = -1 + 1.9881 Reorder the terms: 1.9881 + 2.82x + x2 = -1 + 1.9881 Combine like terms: -1 + 1.9881 = 0.9881 1.9881 + 2.82x + x2 = 0.9881 Factor a perfect square on the left side: (x + 1.41)(x + 1.41) = 0.9881 Calculate the square root of the right side: 0.994032193 Break this problem into two subproblems by setting (x + 1.41) equal to 0.994032193 and -0.994032193.Subproblem 1
x + 1.41 = 0.994032193 Simplifying x + 1.41 = 0.994032193 Reorder the terms: 1.41 + x = 0.994032193 Solving 1.41 + x = 0.994032193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.41' to each side of the equation. 1.41 + -1.41 + x = 0.994032193 + -1.41 Combine like terms: 1.41 + -1.41 = 0.00 0.00 + x = 0.994032193 + -1.41 x = 0.994032193 + -1.41 Combine like terms: 0.994032193 + -1.41 = -0.415967807 x = -0.415967807 Simplifying x = -0.415967807Subproblem 2
x + 1.41 = -0.994032193 Simplifying x + 1.41 = -0.994032193 Reorder the terms: 1.41 + x = -0.994032193 Solving 1.41 + x = -0.994032193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.41' to each side of the equation. 1.41 + -1.41 + x = -0.994032193 + -1.41 Combine like terms: 1.41 + -1.41 = 0.00 0.00 + x = -0.994032193 + -1.41 x = -0.994032193 + -1.41 Combine like terms: -0.994032193 + -1.41 = -2.404032193 x = -2.404032193 Simplifying x = -2.404032193Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.415967807, -2.404032193}
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