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Simplifying x + 0.6x + (0.1666x(0.6x)) = 144.5 Remove parenthesis around (0.6x) x + 0.6x + (0.1666x * 0.6x) = 144.5 Reorder the terms for easier multiplication: x + 0.6x + (0.1666 * 0.6x * x) = 144.5 Multiply 0.1666 * 0.6 x + 0.6x + (0.09996x * x) = 144.5 Multiply x * x x + 0.6x + (0.09996x2) = 144.5 Combine like terms: x + 0.6x = 1.6x 1.6x + (0.09996x2) = 144.5 Solving 1.6x + (0.09996x2) = 144.5 Solving for variable 'x'. Reorder the terms: -144.5 + 1.6x + (0.09996x2) = 144.5 + -144.5 Combine like terms: 144.5 + -144.5 = 0.0 -144.5 + 1.6x + (0.09996x2) = 0.0 Begin completing the square. Divide all terms by 0.09996 the coefficient of the squared term: Divide each side by '0.09996'. -1445.578231 + 16.00640256x + x2 = 0 Move the constant term to the right: Add '1445.578231' to each side of the equation. -1445.578231 + 16.00640256x + 1445.578231 + x2 = 0 + 1445.578231 Reorder the terms: -1445.578231 + 1445.578231 + 16.00640256x + x2 = 0 + 1445.578231 Combine like terms: -1445.578231 + 1445.578231 = 0.000000 0.000000 + 16.00640256x + x2 = 0 + 1445.578231 16.00640256x + x2 = 0 + 1445.578231 Combine like terms: 0 + 1445.578231 = 1445.578231 16.00640256x + x2 = 1445.578231 The x term is 16.00640256x. Take half its coefficient (8.00320128). Square it (64.05123073) and add it to both sides. Add '64.05123073' to each side of the equation. 16.00640256x + 64.05123073 + x2 = 1445.578231 + 64.05123073 Reorder the terms: 64.05123073 + 16.00640256x + x2 = 1445.578231 + 64.05123073 Combine like terms: 1445.578231 + 64.05123073 = 1509.62946173 64.05123073 + 16.00640256x + x2 = 1509.62946173 Factor a perfect square on the left side: ((x) + 8.00320128)((x) + 8.00320128) = 1509.62946173 Calculate the square root of the right side: 38.853950401 Break this problem into two subproblems by setting ((x) + 8.00320128) equal to 38.853950401 and -38.853950401.Subproblem 1
(x) + 8.00320128 = 38.853950401 Simplifying (x) + 8.00320128 = 38.853950401 x + 8.00320128 = 38.853950401 Reorder the terms: 8.00320128 + x = 38.853950401 Solving 8.00320128 + x = 38.853950401 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.00320128' to each side of the equation. 8.00320128 + -8.00320128 + x = 38.853950401 + -8.00320128 Combine like terms: 8.00320128 + -8.00320128 = 0.00000000 0.00000000 + x = 38.853950401 + -8.00320128 x = 38.853950401 + -8.00320128 Combine like terms: 38.853950401 + -8.00320128 = 30.850749121 x = 30.850749121 Simplifying x = 30.850749121Subproblem 2
(x) + 8.00320128 = -38.853950401 Simplifying (x) + 8.00320128 = -38.853950401 x + 8.00320128 = -38.853950401 Reorder the terms: 8.00320128 + x = -38.853950401 Solving 8.00320128 + x = -38.853950401 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.00320128' to each side of the equation. 8.00320128 + -8.00320128 + x = -38.853950401 + -8.00320128 Combine like terms: 8.00320128 + -8.00320128 = 0.00000000 0.00000000 + x = -38.853950401 + -8.00320128 x = -38.853950401 + -8.00320128 Combine like terms: -38.853950401 + -8.00320128 = -46.857151681 x = -46.857151681 Simplifying x = -46.857151681Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.850749121, -46.857151681}
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