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Simplifying 30 = 4.9x2 + 27x + 2.4 Reorder the terms: 30 = 2.4 + 27x + 4.9x2 Solving 30 = 2.4 + 27x + 4.9x2 Solving for variable 'x'. Combine like terms: 30 + -2.4 = 27.6 27.6 + -27x + -4.9x2 = 2.4 + 27x + 4.9x2 + -2.4 + -27x + -4.9x2 Reorder the terms: 27.6 + -27x + -4.9x2 = 2.4 + -2.4 + 27x + -27x + 4.9x2 + -4.9x2 Combine like terms: 2.4 + -2.4 = 0.0 27.6 + -27x + -4.9x2 = 0.0 + 27x + -27x + 4.9x2 + -4.9x2 27.6 + -27x + -4.9x2 = 27x + -27x + 4.9x2 + -4.9x2 Combine like terms: 27x + -27x = 0 27.6 + -27x + -4.9x2 = 0 + 4.9x2 + -4.9x2 27.6 + -27x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 27.6 + -27x + -4.9x2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -5.632653061 + 5.510204082x + x2 = 0 Move the constant term to the right: Add '5.632653061' to each side of the equation. -5.632653061 + 5.510204082x + 5.632653061 + x2 = 0 + 5.632653061 Reorder the terms: -5.632653061 + 5.632653061 + 5.510204082x + x2 = 0 + 5.632653061 Combine like terms: -5.632653061 + 5.632653061 = 0.000000000 0.000000000 + 5.510204082x + x2 = 0 + 5.632653061 5.510204082x + x2 = 0 + 5.632653061 Combine like terms: 0 + 5.632653061 = 5.632653061 5.510204082x + x2 = 5.632653061 The x term is 5.510204082x. Take half its coefficient (2.755102041). Square it (7.590587256) and add it to both sides. Add '7.590587256' to each side of the equation. 5.510204082x + 7.590587256 + x2 = 5.632653061 + 7.590587256 Reorder the terms: 7.590587256 + 5.510204082x + x2 = 5.632653061 + 7.590587256 Combine like terms: 5.632653061 + 7.590587256 = 13.223240317 7.590587256 + 5.510204082x + x2 = 13.223240317 Factor a perfect square on the left side: (x + 2.755102041)(x + 2.755102041) = 13.223240317 Calculate the square root of the right side: 3.636377362 Break this problem into two subproblems by setting (x + 2.755102041) equal to 3.636377362 and -3.636377362.Subproblem 1
x + 2.755102041 = 3.636377362 Simplifying x + 2.755102041 = 3.636377362 Reorder the terms: 2.755102041 + x = 3.636377362 Solving 2.755102041 + x = 3.636377362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.755102041' to each side of the equation. 2.755102041 + -2.755102041 + x = 3.636377362 + -2.755102041 Combine like terms: 2.755102041 + -2.755102041 = 0.000000000 0.000000000 + x = 3.636377362 + -2.755102041 x = 3.636377362 + -2.755102041 Combine like terms: 3.636377362 + -2.755102041 = 0.881275321 x = 0.881275321 Simplifying x = 0.881275321Subproblem 2
x + 2.755102041 = -3.636377362 Simplifying x + 2.755102041 = -3.636377362 Reorder the terms: 2.755102041 + x = -3.636377362 Solving 2.755102041 + x = -3.636377362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.755102041' to each side of the equation. 2.755102041 + -2.755102041 + x = -3.636377362 + -2.755102041 Combine like terms: 2.755102041 + -2.755102041 = 0.000000000 0.000000000 + x = -3.636377362 + -2.755102041 x = -3.636377362 + -2.755102041 Combine like terms: -3.636377362 + -2.755102041 = -6.391479403 x = -6.391479403 Simplifying x = -6.391479403Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.881275321, -6.391479403}
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