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Simplifying 20x2 + 20x + -355 = 0 Reorder the terms: -355 + 20x + 20x2 = 0 Solving -355 + 20x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-71 + 4x + 4x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-71 + 4x + 4x2)' equal to zero and attempt to solve: Simplifying -71 + 4x + 4x2 = 0 Solving -71 + 4x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -17.75 + x + x2 = 0 Move the constant term to the right: Add '17.75' to each side of the equation. -17.75 + x + 17.75 + x2 = 0 + 17.75 Reorder the terms: -17.75 + 17.75 + x + x2 = 0 + 17.75 Combine like terms: -17.75 + 17.75 = 0.00 0.00 + x + x2 = 0 + 17.75 x + x2 = 0 + 17.75 Combine like terms: 0 + 17.75 = 17.75 x + x2 = 17.75 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 17.75 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 17.75 + 0.25 Combine like terms: 17.75 + 0.25 = 18 1.25 + x2 = 18 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x + 0.5) equal to 4.242640687 and -4.242640687.Subproblem 1
x + 0.5 = 4.242640687 Simplifying x + 0.5 = 4.242640687 Reorder the terms: 0.5 + x = 4.242640687 Solving 0.5 + x = 4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4.242640687 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.242640687 + -0.5 x = 4.242640687 + -0.5 Combine like terms: 4.242640687 + -0.5 = 3.742640687 x = 3.742640687 Simplifying x = 3.742640687Subproblem 2
x + 0.5 = -4.242640687 Simplifying x + 0.5 = -4.242640687 Reorder the terms: 0.5 + x = -4.242640687 Solving 0.5 + x = -4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4.242640687 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.242640687 + -0.5 x = -4.242640687 + -0.5 Combine like terms: -4.242640687 + -0.5 = -4.742640687 x = -4.742640687 Simplifying x = -4.742640687Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.742640687, -4.742640687}Solution
x = {3.742640687, -4.742640687}
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