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Simplifying 5x2 + 20x + -17 = 0 Reorder the terms: -17 + 20x + 5x2 = 0 Solving -17 + 20x + 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'. -3.4 + 4x + x2 = 0 Move the constant term to the right: Add '3.4' to each side of the equation. -3.4 + 4x + 3.4 + x2 = 0 + 3.4 Reorder the terms: -3.4 + 3.4 + 4x + x2 = 0 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + 4x + x2 = 0 + 3.4 4x + x2 = 0 + 3.4 Combine like terms: 0 + 3.4 = 3.4 4x + x2 = 3.4 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 3.4 + 4 Reorder the terms: 4 + 4x + x2 = 3.4 + 4 Combine like terms: 3.4 + 4 = 7.4 4 + 4x + x2 = 7.4 Factor a perfect square on the left side: (x + 2)(x + 2) = 7.4 Calculate the square root of the right side: 2.720294102 Break this problem into two subproblems by setting (x + 2) equal to 2.720294102 and -2.720294102.Subproblem 1
x + 2 = 2.720294102 Simplifying x + 2 = 2.720294102 Reorder the terms: 2 + x = 2.720294102 Solving 2 + x = 2.720294102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.720294102 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.720294102 + -2 x = 2.720294102 + -2 Combine like terms: 2.720294102 + -2 = 0.720294102 x = 0.720294102 Simplifying x = 0.720294102Subproblem 2
x + 2 = -2.720294102 Simplifying x + 2 = -2.720294102 Reorder the terms: 2 + x = -2.720294102 Solving 2 + x = -2.720294102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.720294102 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.720294102 + -2 x = -2.720294102 + -2 Combine like terms: -2.720294102 + -2 = -4.720294102 x = -4.720294102 Simplifying x = -4.720294102Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.720294102, -4.720294102}
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