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Simplifying d2 + -19d + 28 = 0 Reorder the terms: 28 + -19d + d2 = 0 Solving 28 + -19d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + -19d + -28 + d2 = 0 + -28 Reorder the terms: 28 + -28 + -19d + d2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -19d + d2 = 0 + -28 -19d + d2 = 0 + -28 Combine like terms: 0 + -28 = -28 -19d + d2 = -28 The d term is -19d. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19d + 90.25 + d2 = -28 + 90.25 Reorder the terms: 90.25 + -19d + d2 = -28 + 90.25 Combine like terms: -28 + 90.25 = 62.25 90.25 + -19d + d2 = 62.25 Factor a perfect square on the left side: (d + -9.5)(d + -9.5) = 62.25 Calculate the square root of the right side: 7.889866919 Break this problem into two subproblems by setting (d + -9.5) equal to 7.889866919 and -7.889866919.Subproblem 1
d + -9.5 = 7.889866919 Simplifying d + -9.5 = 7.889866919 Reorder the terms: -9.5 + d = 7.889866919 Solving -9.5 + d = 7.889866919 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + d = 7.889866919 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + d = 7.889866919 + 9.5 d = 7.889866919 + 9.5 Combine like terms: 7.889866919 + 9.5 = 17.389866919 d = 17.389866919 Simplifying d = 17.389866919Subproblem 2
d + -9.5 = -7.889866919 Simplifying d + -9.5 = -7.889866919 Reorder the terms: -9.5 + d = -7.889866919 Solving -9.5 + d = -7.889866919 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + d = -7.889866919 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + d = -7.889866919 + 9.5 d = -7.889866919 + 9.5 Combine like terms: -7.889866919 + 9.5 = 1.610133081 d = 1.610133081 Simplifying d = 1.610133081Solution
The solution to the problem is based on the solutions from the subproblems. d = {17.389866919, 1.610133081}
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