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Simplifying (d + -4)(d + 0.5) = 0 Reorder the terms: (-4 + d)(d + 0.5) = 0 Reorder the terms: (-4 + d)(0.5 + d) = 0 Multiply (-4 + d) * (0.5 + d) (-4(0.5 + d) + d(0.5 + d)) = 0 ((0.5 * -4 + d * -4) + d(0.5 + d)) = 0 ((-2 + -4d) + d(0.5 + d)) = 0 (-2 + -4d + (0.5 * d + d * d)) = 0 (-2 + -4d + (0.5d + d2)) = 0 Combine like terms: -4d + 0.5d = -3.5d (-2 + -3.5d + d2) = 0 Solving -2 + -3.5d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -3.5d + 2 + d2 = 0 + 2 Reorder the terms: -2 + 2 + -3.5d + d2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3.5d + d2 = 0 + 2 -3.5d + d2 = 0 + 2 Combine like terms: 0 + 2 = 2 -3.5d + d2 = 2 The d term is -3.5d. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5d + 3.0625 + d2 = 2 + 3.0625 Reorder the terms: 3.0625 + -3.5d + d2 = 2 + 3.0625 Combine like terms: 2 + 3.0625 = 5.0625 3.0625 + -3.5d + d2 = 5.0625 Factor a perfect square on the left side: (d + -1.75)(d + -1.75) = 5.0625 Calculate the square root of the right side: 2.25 Break this problem into two subproblems by setting (d + -1.75) equal to 2.25 and -2.25.Subproblem 1
d + -1.75 = 2.25 Simplifying d + -1.75 = 2.25 Reorder the terms: -1.75 + d = 2.25 Solving -1.75 + d = 2.25 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + d = 2.25 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + d = 2.25 + 1.75 d = 2.25 + 1.75 Combine like terms: 2.25 + 1.75 = 4 d = 4 Simplifying d = 4Subproblem 2
d + -1.75 = -2.25 Simplifying d + -1.75 = -2.25 Reorder the terms: -1.75 + d = -2.25 Solving -1.75 + d = -2.25 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + d = -2.25 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + d = -2.25 + 1.75 d = -2.25 + 1.75 Combine like terms: -2.25 + 1.75 = -0.5 d = -0.5 Simplifying d = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. d = {4, -0.5}
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