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Simplifying 2d * d + -10d + -9 = 0 Multiply d * d 2d2 + -10d + -9 = 0 Reorder the terms: -9 + -10d + 2d2 = 0 Solving -9 + -10d + 2d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + -5d + d2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -5d + 4.5 + d2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -5d + d2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -5d + d2 = 0 + 4.5 -5d + d2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -5d + d2 = 4.5 The d term is -5d. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5d + 6.25 + d2 = 4.5 + 6.25 Reorder the terms: 6.25 + -5d + d2 = 4.5 + 6.25 Combine like terms: 4.5 + 6.25 = 10.75 6.25 + -5d + d2 = 10.75 Factor a perfect square on the left side: (d + -2.5)(d + -2.5) = 10.75 Calculate the square root of the right side: 3.278719262 Break this problem into two subproblems by setting (d + -2.5) equal to 3.278719262 and -3.278719262.Subproblem 1
d + -2.5 = 3.278719262 Simplifying d + -2.5 = 3.278719262 Reorder the terms: -2.5 + d = 3.278719262 Solving -2.5 + d = 3.278719262 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + d = 3.278719262 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + d = 3.278719262 + 2.5 d = 3.278719262 + 2.5 Combine like terms: 3.278719262 + 2.5 = 5.778719262 d = 5.778719262 Simplifying d = 5.778719262Subproblem 2
d + -2.5 = -3.278719262 Simplifying d + -2.5 = -3.278719262 Reorder the terms: -2.5 + d = -3.278719262 Solving -2.5 + d = -3.278719262 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + d = -3.278719262 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + d = -3.278719262 + 2.5 d = -3.278719262 + 2.5 Combine like terms: -3.278719262 + 2.5 = -0.778719262 d = -0.778719262 Simplifying d = -0.778719262Solution
The solution to the problem is based on the solutions from the subproblems. d = {5.778719262, -0.778719262}
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