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Simplifying 0.005x2 + -0.02x + -9.66 = 0 Reorder the terms: -9.66 + -0.02x + 0.005x2 = 0 Solving -9.66 + -0.02x + 0.005x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.005 the coefficient of the squared term: Divide each side by '0.005'. -1932 + -4x + x2 = 0 Move the constant term to the right: Add '1932' to each side of the equation. -1932 + -4x + 1932 + x2 = 0 + 1932 Reorder the terms: -1932 + 1932 + -4x + x2 = 0 + 1932 Combine like terms: -1932 + 1932 = 0 0 + -4x + x2 = 0 + 1932 -4x + x2 = 0 + 1932 Combine like terms: 0 + 1932 = 1932 -4x + x2 = 1932 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 1932 + 4 Reorder the terms: 4 + -4x + x2 = 1932 + 4 Combine like terms: 1932 + 4 = 1936 4 + -4x + x2 = 1936 Factor a perfect square on the left side: (x + -2)(x + -2) = 1936 Calculate the square root of the right side: 44 Break this problem into two subproblems by setting (x + -2) equal to 44 and -44.Subproblem 1
x + -2 = 44 Simplifying x + -2 = 44 Reorder the terms: -2 + x = 44 Solving -2 + x = 44 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 44 + 2 Combine like terms: -2 + 2 = 0 0 + x = 44 + 2 x = 44 + 2 Combine like terms: 44 + 2 = 46 x = 46 Simplifying x = 46Subproblem 2
x + -2 = -44 Simplifying x + -2 = -44 Reorder the terms: -2 + x = -44 Solving -2 + x = -44 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -44 + 2 Combine like terms: -2 + 2 = 0 0 + x = -44 + 2 x = -44 + 2 Combine like terms: -44 + 2 = -42 x = -42 Simplifying x = -42Solution
The solution to the problem is based on the solutions from the subproblems. x = {46, -42}
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