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Simplifying 5x2 + 17x + 4 = 0 Reorder the terms: 4 + 17x + 5x2 = 0 Solving 4 + 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'. 0.8 + 3.4x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + 3.4x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + 3.4x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + 3.4x + x2 = 0 + -0.8 3.4x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 3.4x + x2 = -0.8 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 = -0.8 + 2.89 Reorder the terms: 2.89 + 3.4x + x2 = -0.8 + 2.89 Combine like terms: -0.8 + 2.89 = 2.09 2.89 + 3.4x + x2 = 2.09 Factor a perfect square on the left side: (x + 1.7)(x + 1.7) = 2.09 Calculate the square root of the right side: 1.445683229 Break this problem into two subproblems by setting (x + 1.7) equal to 1.445683229 and -1.445683229.Subproblem 1
x + 1.7 = 1.445683229 Simplifying x + 1.7 = 1.445683229 Reorder the terms: 1.7 + x = 1.445683229 Solving 1.7 + x = 1.445683229 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 = 1.445683229 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + x = 1.445683229 + -1.7 x = 1.445683229 + -1.7 Combine like terms: 1.445683229 + -1.7 = -0.254316771 x = -0.254316771 Simplifying x = -0.254316771Subproblem 2
x + 1.7 = -1.445683229 Simplifying x + 1.7 = -1.445683229 Reorder the terms: 1.7 + x = -1.445683229 Solving 1.7 + x = -1.445683229 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 = -1.445683229 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + x = -1.445683229 + -1.7 x = -1.445683229 + -1.7 Combine like terms: -1.445683229 + -1.7 = -3.145683229 x = -3.145683229 Simplifying x = -3.145683229Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.254316771, -3.145683229}
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