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Simplifying 5x2 + 17x + 5 = 0 Reorder the terms: 5 + 17x + 5x2 = 0 Solving 5 + 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'. 1 + 3.4x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 3.4x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 3.4x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3.4x + x2 = 0 + -1 3.4x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 3.4x + x2 = -1 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 = -1 + 2.89 Reorder the terms: 2.89 + 3.4x + x2 = -1 + 2.89 Combine like terms: -1 + 2.89 = 1.89 2.89 + 3.4x + x2 = 1.89 Factor a perfect square on the left side: (x + 1.7)(x + 1.7) = 1.89 Calculate the square root of the right side: 1.374772708 Break this problem into two subproblems by setting (x + 1.7) equal to 1.374772708 and -1.374772708.Subproblem 1
x + 1.7 = 1.374772708 Simplifying x + 1.7 = 1.374772708 Reorder the terms: 1.7 + x = 1.374772708 Solving 1.7 + x = 1.374772708 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 = 1.374772708 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + x = 1.374772708 + -1.7 x = 1.374772708 + -1.7 Combine like terms: 1.374772708 + -1.7 = -0.325227292 x = -0.325227292 Simplifying x = -0.325227292Subproblem 2
x + 1.7 = -1.374772708 Simplifying x + 1.7 = -1.374772708 Reorder the terms: 1.7 + x = -1.374772708 Solving 1.7 + x = -1.374772708 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 = -1.374772708 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + x = -1.374772708 + -1.7 x = -1.374772708 + -1.7 Combine like terms: -1.374772708 + -1.7 = -3.074772708 x = -3.074772708 Simplifying x = -3.074772708Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.325227292, -3.074772708}
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