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Simplifying 14(-19d + -11) * d = 1 Reorder the terms: 14(-11 + -19d) * d = 1 Reorder the terms for easier multiplication: 14d(-11 + -19d) = 1 (-11 * 14d + -19d * 14d) = 1 (-154d + -266d2) = 1 Solving -154d + -266d2 = 1 Solving for variable 'd'. Reorder the terms: -1 + -154d + -266d2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -154d + -266d2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 154d + 266d2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 154d + 266d2)' equal to zero and attempt to solve: Simplifying 1 + 154d + 266d2 = 0 Solving 1 + 154d + 266d2 = 0 Begin completing the square. Divide all terms by 266 the coefficient of the squared term: Divide each side by '266'. 0.003759398496 + 0.5789473684d + d2 = 0 Move the constant term to the right: Add '-0.003759398496' to each side of the equation. 0.003759398496 + 0.5789473684d + -0.003759398496 + d2 = 0 + -0.003759398496 Reorder the terms: 0.003759398496 + -0.003759398496 + 0.5789473684d + d2 = 0 + -0.003759398496 Combine like terms: 0.003759398496 + -0.003759398496 = 0.000000000000 0.000000000000 + 0.5789473684d + d2 = 0 + -0.003759398496 0.5789473684d + d2 = 0 + -0.003759398496 Combine like terms: 0 + -0.003759398496 = -0.003759398496 0.5789473684d + d2 = -0.003759398496 The d term is 0.5789473684d. Take half its coefficient (0.2894736842). Square it (0.08379501384) and add it to both sides. Add '0.08379501384' to each side of the equation. 0.5789473684d + 0.08379501384 + d2 = -0.003759398496 + 0.08379501384 Reorder the terms: 0.08379501384 + 0.5789473684d + d2 = -0.003759398496 + 0.08379501384 Combine like terms: -0.003759398496 + 0.08379501384 = 0.080035615344 0.08379501384 + 0.5789473684d + d2 = 0.080035615344 Factor a perfect square on the left side: (d + 0.2894736842)(d + 0.2894736842) = 0.080035615344 Calculate the square root of the right side: 0.282905665 Break this problem into two subproblems by setting (d + 0.2894736842) equal to 0.282905665 and -0.282905665.Subproblem 1
d + 0.2894736842 = 0.282905665 Simplifying d + 0.2894736842 = 0.282905665 Reorder the terms: 0.2894736842 + d = 0.282905665 Solving 0.2894736842 + d = 0.282905665 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.2894736842' to each side of the equation. 0.2894736842 + -0.2894736842 + d = 0.282905665 + -0.2894736842 Combine like terms: 0.2894736842 + -0.2894736842 = 0.0000000000 0.0000000000 + d = 0.282905665 + -0.2894736842 d = 0.282905665 + -0.2894736842 Combine like terms: 0.282905665 + -0.2894736842 = -0.0065680192 d = -0.0065680192 Simplifying d = -0.0065680192Subproblem 2
d + 0.2894736842 = -0.282905665 Simplifying d + 0.2894736842 = -0.282905665 Reorder the terms: 0.2894736842 + d = -0.282905665 Solving 0.2894736842 + d = -0.282905665 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.2894736842' to each side of the equation. 0.2894736842 + -0.2894736842 + d = -0.282905665 + -0.2894736842 Combine like terms: 0.2894736842 + -0.2894736842 = 0.0000000000 0.0000000000 + d = -0.282905665 + -0.2894736842 d = -0.282905665 + -0.2894736842 Combine like terms: -0.282905665 + -0.2894736842 = -0.5723793492 d = -0.5723793492 Simplifying d = -0.5723793492Solution
The solution to the problem is based on the solutions from the subproblems. d = {-0.0065680192, -0.5723793492}Solution
d = {-0.0065680192, -0.5723793492}
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