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Simplifying 5x2 + 17x + 1 = 0 Reorder the terms: 1 + 17x + 5x2 = 0 Solving 1 + 17x + 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'. 0.2 + 3.4x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + 3.4x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + 3.4x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 3.4x + x2 = 0 + -0.2 3.4x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 3.4x + x2 = -0.2 The x term is 3.4x. Take half its coefficient (1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. 3.4x + 2.89 + x2 = -0.2 + 2.89 Reorder the terms: 2.89 + 3.4x + x2 = -0.2 + 2.89 Combine like terms: -0.2 + 2.89 = 2.69 2.89 + 3.4x + x2 = 2.69 Factor a perfect square on the left side: (x + 1.7)(x + 1.7) = 2.69 Calculate the square root of the right side: 1.640121947 Break this problem into two subproblems by setting (x + 1.7) equal to 1.640121947 and -1.640121947.Subproblem 1
x + 1.7 = 1.640121947 Simplifying x + 1.7 = 1.640121947 Reorder the terms: 1.7 + x = 1.640121947 Solving 1.7 + x = 1.640121947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + x = 1.640121947 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + x = 1.640121947 + -1.7 x = 1.640121947 + -1.7 Combine like terms: 1.640121947 + -1.7 = -0.059878053 x = -0.059878053 Simplifying x = -0.059878053Subproblem 2
x + 1.7 = -1.640121947 Simplifying x + 1.7 = -1.640121947 Reorder the terms: 1.7 + x = -1.640121947 Solving 1.7 + x = -1.640121947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + x = -1.640121947 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + x = -1.640121947 + -1.7 x = -1.640121947 + -1.7 Combine like terms: -1.640121947 + -1.7 = -3.340121947 x = -3.340121947 Simplifying x = -3.340121947Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.059878053, -3.340121947}
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