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Simplifying 0.1x2 + -4x + -0.5 = 0 Reorder the terms: -0.5 + -4x + 0.1x2 = 0 Solving -0.5 + -4x + 0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. -5 + -40x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -40x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -40x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -40x + x2 = 0 + 5 -40x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -40x + x2 = 5 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = 5 + 400 Reorder the terms: 400 + -40x + x2 = 5 + 400 Combine like terms: 5 + 400 = 405 400 + -40x + x2 = 405 Factor a perfect square on the left side: (x + -20)(x + -20) = 405 Calculate the square root of the right side: 20.124611797 Break this problem into two subproblems by setting (x + -20) equal to 20.124611797 and -20.124611797.Subproblem 1
x + -20 = 20.124611797 Simplifying x + -20 = 20.124611797 Reorder the terms: -20 + x = 20.124611797 Solving -20 + x = 20.124611797 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 20.124611797 + 20 Combine like terms: -20 + 20 = 0 0 + x = 20.124611797 + 20 x = 20.124611797 + 20 Combine like terms: 20.124611797 + 20 = 40.124611797 x = 40.124611797 Simplifying x = 40.124611797Subproblem 2
x + -20 = -20.124611797 Simplifying x + -20 = -20.124611797 Reorder the terms: -20 + x = -20.124611797 Solving -20 + x = -20.124611797 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -20.124611797 + 20 Combine like terms: -20 + 20 = 0 0 + x = -20.124611797 + 20 x = -20.124611797 + 20 Combine like terms: -20.124611797 + 20 = -0.124611797 x = -0.124611797 Simplifying x = -0.124611797Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.124611797, -0.124611797}
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