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Simplifying 0.05x2 + 0.1x + -80 = 0 Reorder the terms: -80 + 0.1x + 0.05x2 = 0 Solving -80 + 0.1x + 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'. -1600 + 2x + x2 = 0 Move the constant term to the right: Add '1600' to each side of the equation. -1600 + 2x + 1600 + x2 = 0 + 1600 Reorder the terms: -1600 + 1600 + 2x + x2 = 0 + 1600 Combine like terms: -1600 + 1600 = 0 0 + 2x + x2 = 0 + 1600 2x + x2 = 0 + 1600 Combine like terms: 0 + 1600 = 1600 2x + x2 = 1600 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 = 1600 + 1 Reorder the terms: 1 + 2x + x2 = 1600 + 1 Combine like terms: 1600 + 1 = 1601 1 + 2x + x2 = 1601 Factor a perfect square on the left side: (x + 1)(x + 1) = 1601 Calculate the square root of the right side: 40.012498047 Break this problem into two subproblems by setting (x + 1) equal to 40.012498047 and -40.012498047.Subproblem 1
x + 1 = 40.012498047 Simplifying x + 1 = 40.012498047 Reorder the terms: 1 + x = 40.012498047 Solving 1 + x = 40.012498047 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 = 40.012498047 + -1 Combine like terms: 1 + -1 = 0 0 + x = 40.012498047 + -1 x = 40.012498047 + -1 Combine like terms: 40.012498047 + -1 = 39.012498047 x = 39.012498047 Simplifying x = 39.012498047Subproblem 2
x + 1 = -40.012498047 Simplifying x + 1 = -40.012498047 Reorder the terms: 1 + x = -40.012498047 Solving 1 + x = -40.012498047 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 = -40.012498047 + -1 Combine like terms: 1 + -1 = 0 0 + x = -40.012498047 + -1 x = -40.012498047 + -1 Combine like terms: -40.012498047 + -1 = -41.012498047 x = -41.012498047 Simplifying x = -41.012498047Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.012498047, -41.012498047}
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