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Simplifying 0 = 0.81x2 + -5x + -6000 Reorder the terms: 0 = -6000 + -5x + 0.81x2 Solving 0 = -6000 + -5x + 0.81x2 Solving for variable 'x'. Combine like terms: 0 + 6000 = 6000 6000 + 5x + -0.81x2 = -6000 + -5x + 0.81x2 + 6000 + 5x + -0.81x2 Reorder the terms: 6000 + 5x + -0.81x2 = -6000 + 6000 + -5x + 5x + 0.81x2 + -0.81x2 Combine like terms: -6000 + 6000 = 0 6000 + 5x + -0.81x2 = 0 + -5x + 5x + 0.81x2 + -0.81x2 6000 + 5x + -0.81x2 = -5x + 5x + 0.81x2 + -0.81x2 Combine like terms: -5x + 5x = 0 6000 + 5x + -0.81x2 = 0 + 0.81x2 + -0.81x2 6000 + 5x + -0.81x2 = 0.81x2 + -0.81x2 Combine like terms: 0.81x2 + -0.81x2 = 0.00 6000 + 5x + -0.81x2 = 0.00 Begin completing the square. Divide all terms by -0.81 the coefficient of the squared term: Divide each side by '-0.81'. -7407.407407 + -6.172839506x + x2 = 0 Move the constant term to the right: Add '7407.407407' to each side of the equation. -7407.407407 + -6.172839506x + 7407.407407 + x2 = 0 + 7407.407407 Reorder the terms: -7407.407407 + 7407.407407 + -6.172839506x + x2 = 0 + 7407.407407 Combine like terms: -7407.407407 + 7407.407407 = 0.000000 0.000000 + -6.172839506x + x2 = 0 + 7407.407407 -6.172839506x + x2 = 0 + 7407.407407 Combine like terms: 0 + 7407.407407 = 7407.407407 -6.172839506x + x2 = 7407.407407 The x term is -6.172839506x. Take half its coefficient (-3.086419753). Square it (9.525986892) and add it to both sides. Add '9.525986892' to each side of the equation. -6.172839506x + 9.525986892 + x2 = 7407.407407 + 9.525986892 Reorder the terms: 9.525986892 + -6.172839506x + x2 = 7407.407407 + 9.525986892 Combine like terms: 7407.407407 + 9.525986892 = 7416.933393892 9.525986892 + -6.172839506x + x2 = 7416.933393892 Factor a perfect square on the left side: (x + -3.086419753)(x + -3.086419753) = 7416.933393892 Calculate the square root of the right side: 86.121619782 Break this problem into two subproblems by setting (x + -3.086419753) equal to 86.121619782 and -86.121619782.Subproblem 1
x + -3.086419753 = 86.121619782 Simplifying x + -3.086419753 = 86.121619782 Reorder the terms: -3.086419753 + x = 86.121619782 Solving -3.086419753 + x = 86.121619782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.086419753' to each side of the equation. -3.086419753 + 3.086419753 + x = 86.121619782 + 3.086419753 Combine like terms: -3.086419753 + 3.086419753 = 0.000000000 0.000000000 + x = 86.121619782 + 3.086419753 x = 86.121619782 + 3.086419753 Combine like terms: 86.121619782 + 3.086419753 = 89.208039535 x = 89.208039535 Simplifying x = 89.208039535Subproblem 2
x + -3.086419753 = -86.121619782 Simplifying x + -3.086419753 = -86.121619782 Reorder the terms: -3.086419753 + x = -86.121619782 Solving -3.086419753 + x = -86.121619782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.086419753' to each side of the equation. -3.086419753 + 3.086419753 + x = -86.121619782 + 3.086419753 Combine like terms: -3.086419753 + 3.086419753 = 0.000000000 0.000000000 + x = -86.121619782 + 3.086419753 x = -86.121619782 + 3.086419753 Combine like terms: -86.121619782 + 3.086419753 = -83.035200029 x = -83.035200029 Simplifying x = -83.035200029Solution
The solution to the problem is based on the solutions from the subproblems. x = {89.208039535, -83.035200029}
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