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Simplifying 7d(2d + -3) = 6d + 3 Reorder the terms: 7d(-3 + 2d) = 6d + 3 (-3 * 7d + 2d * 7d) = 6d + 3 (-21d + 14d2) = 6d + 3 Reorder the terms: -21d + 14d2 = 3 + 6d Solving -21d + 14d2 = 3 + 6d Solving for variable 'd'. Reorder the terms: -3 + -21d + -6d + 14d2 = 3 + 6d + -3 + -6d Combine like terms: -21d + -6d = -27d -3 + -27d + 14d2 = 3 + 6d + -3 + -6d Reorder the terms: -3 + -27d + 14d2 = 3 + -3 + 6d + -6d Combine like terms: 3 + -3 = 0 -3 + -27d + 14d2 = 0 + 6d + -6d -3 + -27d + 14d2 = 6d + -6d Combine like terms: 6d + -6d = 0 -3 + -27d + 14d2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.2142857143 + -1.928571429d + d2 = 0 Move the constant term to the right: Add '0.2142857143' to each side of the equation. -0.2142857143 + -1.928571429d + 0.2142857143 + d2 = 0 + 0.2142857143 Reorder the terms: -0.2142857143 + 0.2142857143 + -1.928571429d + d2 = 0 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + -1.928571429d + d2 = 0 + 0.2142857143 -1.928571429d + d2 = 0 + 0.2142857143 Combine like terms: 0 + 0.2142857143 = 0.2142857143 -1.928571429d + d2 = 0.2142857143 The d term is -1.928571429d. Take half its coefficient (-0.9642857145). Square it (0.9298469392) and add it to both sides. Add '0.9298469392' to each side of the equation. -1.928571429d + 0.9298469392 + d2 = 0.2142857143 + 0.9298469392 Reorder the terms: 0.9298469392 + -1.928571429d + d2 = 0.2142857143 + 0.9298469392 Combine like terms: 0.2142857143 + 0.9298469392 = 1.1441326535 0.9298469392 + -1.928571429d + d2 = 1.1441326535 Factor a perfect square on the left side: (d + -0.9642857145)(d + -0.9642857145) = 1.1441326535 Calculate the square root of the right side: 1.069641367 Break this problem into two subproblems by setting (d + -0.9642857145) equal to 1.069641367 and -1.069641367.Subproblem 1
d + -0.9642857145 = 1.069641367 Simplifying d + -0.9642857145 = 1.069641367 Reorder the terms: -0.9642857145 + d = 1.069641367 Solving -0.9642857145 + d = 1.069641367 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.9642857145' to each side of the equation. -0.9642857145 + 0.9642857145 + d = 1.069641367 + 0.9642857145 Combine like terms: -0.9642857145 + 0.9642857145 = 0.0000000000 0.0000000000 + d = 1.069641367 + 0.9642857145 d = 1.069641367 + 0.9642857145 Combine like terms: 1.069641367 + 0.9642857145 = 2.0339270815 d = 2.0339270815 Simplifying d = 2.0339270815Subproblem 2
d + -0.9642857145 = -1.069641367 Simplifying d + -0.9642857145 = -1.069641367 Reorder the terms: -0.9642857145 + d = -1.069641367 Solving -0.9642857145 + d = -1.069641367 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.9642857145' to each side of the equation. -0.9642857145 + 0.9642857145 + d = -1.069641367 + 0.9642857145 Combine like terms: -0.9642857145 + 0.9642857145 = 0.0000000000 0.0000000000 + d = -1.069641367 + 0.9642857145 d = -1.069641367 + 0.9642857145 Combine like terms: -1.069641367 + 0.9642857145 = -0.1053556525 d = -0.1053556525 Simplifying d = -0.1053556525Solution
The solution to the problem is based on the solutions from the subproblems. d = {2.0339270815, -0.1053556525}
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