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Simplifying 0 = -21.7 + 64999.78x + -0.018x2 Solving 0 = -21.7 + 64999.78x + -0.018x2 Solving for variable 'x'. Combine like terms: 0 + 21.7 = 21.7 21.7 + -64999.78x + 0.018x2 = -21.7 + 64999.78x + -0.018x2 + 21.7 + -64999.78x + 0.018x2 Reorder the terms: 21.7 + -64999.78x + 0.018x2 = -21.7 + 21.7 + 64999.78x + -64999.78x + -0.018x2 + 0.018x2 Combine like terms: -21.7 + 21.7 = 0.0 21.7 + -64999.78x + 0.018x2 = 0.0 + 64999.78x + -64999.78x + -0.018x2 + 0.018x2 21.7 + -64999.78x + 0.018x2 = 64999.78x + -64999.78x + -0.018x2 + 0.018x2 Combine like terms: 64999.78x + -64999.78x = 0.00 21.7 + -64999.78x + 0.018x2 = 0.00 + -0.018x2 + 0.018x2 21.7 + -64999.78x + 0.018x2 = -0.018x2 + 0.018x2 Combine like terms: -0.018x2 + 0.018x2 = 0.000 21.7 + -64999.78x + 0.018x2 = 0.000 Begin completing the square. Divide all terms by 0.018 the coefficient of the squared term: Divide each side by '0.018'. 1205.555556 + -3611098.889x + x2 = 0 Move the constant term to the right: Add '-1205.555556' to each side of the equation. 1205.555556 + -3611098.889x + -1205.555556 + x2 = 0 + -1205.555556 Reorder the terms: 1205.555556 + -1205.555556 + -3611098.889x + x2 = 0 + -1205.555556 Combine like terms: 1205.555556 + -1205.555556 = 0.000000 0.000000 + -3611098.889x + x2 = 0 + -1205.555556 -3611098.889x + x2 = 0 + -1205.555556 Combine like terms: 0 + -1205.555556 = -1205.555556 -3611098.889x + x2 = -1205.555556 The x term is -3611098.889x. Take half its coefficient (-1805549.445). Square it (3260008798000) and add it to both sides. Add '3260008798000' to each side of the equation. -3611098.889x + 3260008798000 + x2 = -1205.555556 + 3260008798000 Reorder the terms: 3260008798000 + -3611098.889x + x2 = -1205.555556 + 3260008798000 Combine like terms: -1205.555556 + 3260008798000 = 3260008796794.444444 3260008798000 + -3611098.889x + x2 = 3260008796794.444444 Factor a perfect square on the left side: (x + -1805549.445)(x + -1805549.445) = 3260008796794.444444 Calculate the square root of the right side: 1805549.444572052 Break this problem into two subproblems by setting (x + -1805549.445) equal to 1805549.444572052 and -1805549.444572052.Subproblem 1
x + -1805549.445 = 1805549.444572052 Simplifying x + -1805549.445 = 1805549.444572052 Reorder the terms: -1805549.445 + x = 1805549.444572052 Solving -1805549.445 + x = 1805549.444572052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1805549.445' to each side of the equation. -1805549.445 + 1805549.445 + x = 1805549.444572052 + 1805549.445 Combine like terms: -1805549.445 + 1805549.445 = 0.000 0.000 + x = 1805549.444572052 + 1805549.445 x = 1805549.444572052 + 1805549.445 Combine like terms: 1805549.444572052 + 1805549.445 = 3611098.889572052 x = 3611098.889572052 Simplifying x = 3611098.889572052Subproblem 2
x + -1805549.445 = -1805549.444572052 Simplifying x + -1805549.445 = -1805549.444572052 Reorder the terms: -1805549.445 + x = -1805549.444572052 Solving -1805549.445 + x = -1805549.444572052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1805549.445' to each side of the equation. -1805549.445 + 1805549.445 + x = -1805549.444572052 + 1805549.445 Combine like terms: -1805549.445 + 1805549.445 = 0.000 0.000 + x = -1805549.444572052 + 1805549.445 x = -1805549.444572052 + 1805549.445 Combine like terms: -1805549.444572052 + 1805549.445 = 0.000427948 x = 0.000427948 Simplifying x = 0.000427948Solution
The solution to the problem is based on the solutions from the subproblems. x = {3611098.889572052, 0.000427948}
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