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Simplifying 8 = (3 + 0.36x) * x Reorder the terms for easier multiplication: 8 = x(3 + 0.36x) 8 = (3 * x + 0.36x * x) 8 = (3x + 0.36x2) Solving 8 = 3x + 0.36x2 Solving for variable 'x'. Reorder the terms: 8 + -3x + -0.36x2 = 3x + -3x + 0.36x2 + -0.36x2 Combine like terms: 3x + -3x = 0 8 + -3x + -0.36x2 = 0 + 0.36x2 + -0.36x2 8 + -3x + -0.36x2 = 0.36x2 + -0.36x2 Combine like terms: 0.36x2 + -0.36x2 = 0.00 8 + -3x + -0.36x2 = 0.00 Begin completing the square. Divide all terms by -0.36 the coefficient of the squared term: Divide each side by '-0.36'. -22.22222222 + 8.333333333x + x2 = 0 Move the constant term to the right: Add '22.22222222' to each side of the equation. -22.22222222 + 8.333333333x + 22.22222222 + x2 = 0 + 22.22222222 Reorder the terms: -22.22222222 + 22.22222222 + 8.333333333x + x2 = 0 + 22.22222222 Combine like terms: -22.22222222 + 22.22222222 = 0.00000000 0.00000000 + 8.333333333x + x2 = 0 + 22.22222222 8.333333333x + x2 = 0 + 22.22222222 Combine like terms: 0 + 22.22222222 = 22.22222222 8.333333333x + x2 = 22.22222222 The x term is 8.333333333x. Take half its coefficient (4.166666667). Square it (17.36111111) and add it to both sides. Add '17.36111111' to each side of the equation. 8.333333333x + 17.36111111 + x2 = 22.22222222 + 17.36111111 Reorder the terms: 17.36111111 + 8.333333333x + x2 = 22.22222222 + 17.36111111 Combine like terms: 22.22222222 + 17.36111111 = 39.58333333 17.36111111 + 8.333333333x + x2 = 39.58333333 Factor a perfect square on the left side: (x + 4.166666667)(x + 4.166666667) = 39.58333333 Calculate the square root of the right side: 6.291528696 Break this problem into two subproblems by setting (x + 4.166666667) equal to 6.291528696 and -6.291528696.Subproblem 1
x + 4.166666667 = 6.291528696 Simplifying x + 4.166666667 = 6.291528696 Reorder the terms: 4.166666667 + x = 6.291528696 Solving 4.166666667 + x = 6.291528696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.166666667' to each side of the equation. 4.166666667 + -4.166666667 + x = 6.291528696 + -4.166666667 Combine like terms: 4.166666667 + -4.166666667 = 0.000000000 0.000000000 + x = 6.291528696 + -4.166666667 x = 6.291528696 + -4.166666667 Combine like terms: 6.291528696 + -4.166666667 = 2.124862029 x = 2.124862029 Simplifying x = 2.124862029Subproblem 2
x + 4.166666667 = -6.291528696 Simplifying x + 4.166666667 = -6.291528696 Reorder the terms: 4.166666667 + x = -6.291528696 Solving 4.166666667 + x = -6.291528696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.166666667' to each side of the equation. 4.166666667 + -4.166666667 + x = -6.291528696 + -4.166666667 Combine like terms: 4.166666667 + -4.166666667 = 0.000000000 0.000000000 + x = -6.291528696 + -4.166666667 x = -6.291528696 + -4.166666667 Combine like terms: -6.291528696 + -4.166666667 = -10.458195363 x = -10.458195363 Simplifying x = -10.458195363Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.124862029, -10.458195363}
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