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Simplifying 0.3(d + -2) * 0.8d = 4.4 Reorder the terms: 0.3(-2 + d) * 0.8d = 4.4 Reorder the terms for easier multiplication: 0.3 * 0.8d(-2 + d) = 4.4 Multiply 0.3 * 0.8 0.24d(-2 + d) = 4.4 (-2 * 0.24d + d * 0.24d) = 4.4 (-0.48d + 0.24d2) = 4.4 Solving -0.48d + 0.24d2 = 4.4 Solving for variable 'd'. Reorder the terms: -4.4 + -0.48d + 0.24d2 = 4.4 + -4.4 Combine like terms: 4.4 + -4.4 = 0.0 -4.4 + -0.48d + 0.24d2 = 0.0 Begin completing the square. Divide all terms by 0.24 the coefficient of the squared term: Divide each side by '0.24'. -18.33333333 + -2d + d2 = 0 Move the constant term to the right: Add '18.33333333' to each side of the equation. -18.33333333 + -2d + 18.33333333 + d2 = 0 + 18.33333333 Reorder the terms: -18.33333333 + 18.33333333 + -2d + d2 = 0 + 18.33333333 Combine like terms: -18.33333333 + 18.33333333 = 0.00000000 0.00000000 + -2d + d2 = 0 + 18.33333333 -2d + d2 = 0 + 18.33333333 Combine like terms: 0 + 18.33333333 = 18.33333333 -2d + d2 = 18.33333333 The d term is -2d. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2d + 1 + d2 = 18.33333333 + 1 Reorder the terms: 1 + -2d + d2 = 18.33333333 + 1 Combine like terms: 18.33333333 + 1 = 19.33333333 1 + -2d + d2 = 19.33333333 Factor a perfect square on the left side: (d + -1)(d + -1) = 19.33333333 Calculate the square root of the right side: 4.396968652 Break this problem into two subproblems by setting (d + -1) equal to 4.396968652 and -4.396968652.Subproblem 1
d + -1 = 4.396968652 Simplifying d + -1 = 4.396968652 Reorder the terms: -1 + d = 4.396968652 Solving -1 + d = 4.396968652 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + d = 4.396968652 + 1 Combine like terms: -1 + 1 = 0 0 + d = 4.396968652 + 1 d = 4.396968652 + 1 Combine like terms: 4.396968652 + 1 = 5.396968652 d = 5.396968652 Simplifying d = 5.396968652Subproblem 2
d + -1 = -4.396968652 Simplifying d + -1 = -4.396968652 Reorder the terms: -1 + d = -4.396968652 Solving -1 + d = -4.396968652 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + d = -4.396968652 + 1 Combine like terms: -1 + 1 = 0 0 + d = -4.396968652 + 1 d = -4.396968652 + 1 Combine like terms: -4.396968652 + 1 = -3.396968652 d = -3.396968652 Simplifying d = -3.396968652Solution
The solution to the problem is based on the solutions from the subproblems. d = {5.396968652, -3.396968652}
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