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Simplifying 28000 = 2297d2 + 18378d Reorder the terms: 28000 = 18378d + 2297d2 Solving 28000 = 18378d + 2297d2 Solving for variable 'd'. Reorder the terms: 28000 + -18378d + -2297d2 = 18378d + -18378d + 2297d2 + -2297d2 Combine like terms: 18378d + -18378d = 0 28000 + -18378d + -2297d2 = 0 + 2297d2 + -2297d2 28000 + -18378d + -2297d2 = 2297d2 + -2297d2 Combine like terms: 2297d2 + -2297d2 = 0 28000 + -18378d + -2297d2 = 0 Begin completing the square. Divide all terms by -2297 the coefficient of the squared term: Divide each side by '-2297'. -12.1898128 + 8.000870701d + d2 = 0 Move the constant term to the right: Add '12.1898128' to each side of the equation. -12.1898128 + 8.000870701d + 12.1898128 + d2 = 0 + 12.1898128 Reorder the terms: -12.1898128 + 12.1898128 + 8.000870701d + d2 = 0 + 12.1898128 Combine like terms: -12.1898128 + 12.1898128 = 0.0000000 0.0000000 + 8.000870701d + d2 = 0 + 12.1898128 8.000870701d + d2 = 0 + 12.1898128 Combine like terms: 0 + 12.1898128 = 12.1898128 8.000870701d + d2 = 12.1898128 The d term is 8.000870701d. Take half its coefficient (4.000435351). Square it (16.00348300) and add it to both sides. Add '16.00348300' to each side of the equation. 8.000870701d + 16.00348300 + d2 = 12.1898128 + 16.00348300 Reorder the terms: 16.00348300 + 8.000870701d + d2 = 12.1898128 + 16.00348300 Combine like terms: 12.1898128 + 16.00348300 = 28.1932958 16.00348300 + 8.000870701d + d2 = 28.1932958 Factor a perfect square on the left side: (d + 4.000435351)(d + 4.000435351) = 28.1932958 Calculate the square root of the right side: 5.309735944 Break this problem into two subproblems by setting (d + 4.000435351) equal to 5.309735944 and -5.309735944.Subproblem 1
d + 4.000435351 = 5.309735944 Simplifying d + 4.000435351 = 5.309735944 Reorder the terms: 4.000435351 + d = 5.309735944 Solving 4.000435351 + d = 5.309735944 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-4.000435351' to each side of the equation. 4.000435351 + -4.000435351 + d = 5.309735944 + -4.000435351 Combine like terms: 4.000435351 + -4.000435351 = 0.000000000 0.000000000 + d = 5.309735944 + -4.000435351 d = 5.309735944 + -4.000435351 Combine like terms: 5.309735944 + -4.000435351 = 1.309300593 d = 1.309300593 Simplifying d = 1.309300593Subproblem 2
d + 4.000435351 = -5.309735944 Simplifying d + 4.000435351 = -5.309735944 Reorder the terms: 4.000435351 + d = -5.309735944 Solving 4.000435351 + d = -5.309735944 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-4.000435351' to each side of the equation. 4.000435351 + -4.000435351 + d = -5.309735944 + -4.000435351 Combine like terms: 4.000435351 + -4.000435351 = 0.000000000 0.000000000 + d = -5.309735944 + -4.000435351 d = -5.309735944 + -4.000435351 Combine like terms: -5.309735944 + -4.000435351 = -9.310171295 d = -9.310171295 Simplifying d = -9.310171295Solution
The solution to the problem is based on the solutions from the subproblems. d = {1.309300593, -9.310171295}
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