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Simplifying 4x2 + 20x + 17 = 0 Reorder the terms: 17 + 20x + 4x2 = 0 Solving 17 + 20x + 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'. 4.25 + 5x + x2 = 0 Move the constant term to the right: Add '-4.25' to each side of the equation. 4.25 + 5x + -4.25 + x2 = 0 + -4.25 Reorder the terms: 4.25 + -4.25 + 5x + x2 = 0 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + 5x + x2 = 0 + -4.25 5x + x2 = 0 + -4.25 Combine like terms: 0 + -4.25 = -4.25 5x + x2 = -4.25 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -4.25 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -4.25 + 6.25 Combine like terms: -4.25 + 6.25 = 2 6.25 + 5x + x2 = 2 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + 2.5) equal to 1.414213562 and -1.414213562.Subproblem 1
x + 2.5 = 1.414213562 Simplifying x + 2.5 = 1.414213562 Reorder the terms: 2.5 + x = 1.414213562 Solving 2.5 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 1.414213562 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 1.414213562 + -2.5 x = 1.414213562 + -2.5 Combine like terms: 1.414213562 + -2.5 = -1.085786438 x = -1.085786438 Simplifying x = -1.085786438Subproblem 2
x + 2.5 = -1.414213562 Simplifying x + 2.5 = -1.414213562 Reorder the terms: 2.5 + x = -1.414213562 Solving 2.5 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -1.414213562 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -1.414213562 + -2.5 x = -1.414213562 + -2.5 Combine like terms: -1.414213562 + -2.5 = -3.914213562 x = -3.914213562 Simplifying x = -3.914213562Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.085786438, -3.914213562}
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