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Simplifying (2.5(x2)) + -20x + 2 = 0 Reorder the terms: 2 + -20x + (2.5x2) = 0 Solving 2 + -20x + (2.5x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. 0.8 + -8x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -8x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -8x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -8x + x2 = 0 + -0.8 -8x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -8x + x2 = -0.8 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -0.8 + 16 Reorder the terms: 16 + -8x + x2 = -0.8 + 16 Combine like terms: -0.8 + 16 = 15.2 16 + -8x + x2 = 15.2 Factor a perfect square on the left side: ((x) + -4)((x) + -4) = 15.2 Calculate the square root of the right side: 3.898717738 Break this problem into two subproblems by setting ((x) + -4) equal to 3.898717738 and -3.898717738.Subproblem 1
(x) + -4 = 3.898717738 Simplifying (x) + -4 = 3.898717738 x + -4 = 3.898717738 Reorder the terms: -4 + x = 3.898717738 Solving -4 + x = 3.898717738 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3.898717738 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.898717738 + 4 x = 3.898717738 + 4 Combine like terms: 3.898717738 + 4 = 7.898717738 x = 7.898717738 Simplifying x = 7.898717738Subproblem 2
(x) + -4 = -3.898717738 Simplifying (x) + -4 = -3.898717738 x + -4 = -3.898717738 Reorder the terms: -4 + x = -3.898717738 Solving -4 + x = -3.898717738 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3.898717738 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.898717738 + 4 x = -3.898717738 + 4 Combine like terms: -3.898717738 + 4 = 0.101282262 x = 0.101282262 Simplifying x = 0.101282262Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.898717738, 0.101282262}
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