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Simplifying 4x2 + 17x + 5 = 0 Reorder the terms: 5 + 17x + 4x2 = 0 Solving 5 + 17x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 4.25x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 4.25x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 4.25x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 4.25x + x2 = 0 + -1.25 4.25x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 4.25x + x2 = -1.25 The x term is 4.25x. Take half its coefficient (2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. 4.25x + 4.515625 + x2 = -1.25 + 4.515625 Reorder the terms: 4.515625 + 4.25x + x2 = -1.25 + 4.515625 Combine like terms: -1.25 + 4.515625 = 3.265625 4.515625 + 4.25x + x2 = 3.265625 Factor a perfect square on the left side: (x + 2.125)(x + 2.125) = 3.265625 Calculate the square root of the right side: 1.807104037 Break this problem into two subproblems by setting (x + 2.125) equal to 1.807104037 and -1.807104037.Subproblem 1
x + 2.125 = 1.807104037 Simplifying x + 2.125 = 1.807104037 Reorder the terms: 2.125 + x = 1.807104037 Solving 2.125 + x = 1.807104037 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = 1.807104037 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = 1.807104037 + -2.125 x = 1.807104037 + -2.125 Combine like terms: 1.807104037 + -2.125 = -0.317895963 x = -0.317895963 Simplifying x = -0.317895963Subproblem 2
x + 2.125 = -1.807104037 Simplifying x + 2.125 = -1.807104037 Reorder the terms: 2.125 + x = -1.807104037 Solving 2.125 + x = -1.807104037 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = -1.807104037 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = -1.807104037 + -2.125 x = -1.807104037 + -2.125 Combine like terms: -1.807104037 + -2.125 = -3.932104037 x = -3.932104037 Simplifying x = -3.932104037Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.317895963, -3.932104037}
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