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Simplifying 20x2 + 40x + 17 = 0 Reorder the terms: 17 + 40x + 20x2 = 0 Solving 17 + 40x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.85 + 2x + x2 = 0 Move the constant term to the right: Add '-0.85' to each side of the equation. 0.85 + 2x + -0.85 + x2 = 0 + -0.85 Reorder the terms: 0.85 + -0.85 + 2x + x2 = 0 + -0.85 Combine like terms: 0.85 + -0.85 = 0.00 0.00 + 2x + x2 = 0 + -0.85 2x + x2 = 0 + -0.85 Combine like terms: 0 + -0.85 = -0.85 2x + x2 = -0.85 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -0.85 + 1 Reorder the terms: 1 + 2x + x2 = -0.85 + 1 Combine like terms: -0.85 + 1 = 0.15 1 + 2x + x2 = 0.15 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.15 Calculate the square root of the right side: 0.387298335 Break this problem into two subproblems by setting (x + 1) equal to 0.387298335 and -0.387298335.Subproblem 1
x + 1 = 0.387298335 Simplifying x + 1 = 0.387298335 Reorder the terms: 1 + x = 0.387298335 Solving 1 + x = 0.387298335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.387298335 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.387298335 + -1 x = 0.387298335 + -1 Combine like terms: 0.387298335 + -1 = -0.612701665 x = -0.612701665 Simplifying x = -0.612701665Subproblem 2
x + 1 = -0.387298335 Simplifying x + 1 = -0.387298335 Reorder the terms: 1 + x = -0.387298335 Solving 1 + x = -0.387298335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.387298335 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.387298335 + -1 x = -0.387298335 + -1 Combine like terms: -0.387298335 + -1 = -1.387298335 x = -1.387298335 Simplifying x = -1.387298335Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.612701665, -1.387298335}
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