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Simplifying 0.05x2 + -0.5x + 0.08 = 0 Reorder the terms: 0.08 + -0.5x + 0.05x2 = 0 Solving 0.08 + -0.5x + 0.05x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. 1.6 + -10x + x2 = 0 Move the constant term to the right: Add '-1.6' to each side of the equation. 1.6 + -10x + -1.6 + x2 = 0 + -1.6 Reorder the terms: 1.6 + -1.6 + -10x + x2 = 0 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + -10x + x2 = 0 + -1.6 -10x + x2 = 0 + -1.6 Combine like terms: 0 + -1.6 = -1.6 -10x + x2 = -1.6 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -1.6 + 25 Reorder the terms: 25 + -10x + x2 = -1.6 + 25 Combine like terms: -1.6 + 25 = 23.4 25 + -10x + x2 = 23.4 Factor a perfect square on the left side: (x + -5)(x + -5) = 23.4 Calculate the square root of the right side: 4.837354649 Break this problem into two subproblems by setting (x + -5) equal to 4.837354649 and -4.837354649.Subproblem 1
x + -5 = 4.837354649 Simplifying x + -5 = 4.837354649 Reorder the terms: -5 + x = 4.837354649 Solving -5 + x = 4.837354649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 4.837354649 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.837354649 + 5 x = 4.837354649 + 5 Combine like terms: 4.837354649 + 5 = 9.837354649 x = 9.837354649 Simplifying x = 9.837354649Subproblem 2
x + -5 = -4.837354649 Simplifying x + -5 = -4.837354649 Reorder the terms: -5 + x = -4.837354649 Solving -5 + x = -4.837354649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -4.837354649 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.837354649 + 5 x = -4.837354649 + 5 Combine like terms: -4.837354649 + 5 = 0.162645351 x = 0.162645351 Simplifying x = 0.162645351Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.837354649, 0.162645351}
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