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Simplifying 18x2 + 4x = 21 Reorder the terms: 4x + 18x2 = 21 Solving 4x + 18x2 = 21 Solving for variable 'x'. Reorder the terms: -21 + 4x + 18x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + 4x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -1.166666667 + 0.2222222222x + x2 = 0 Move the constant term to the right: Add '1.166666667' to each side of the equation. -1.166666667 + 0.2222222222x + 1.166666667 + x2 = 0 + 1.166666667 Reorder the terms: -1.166666667 + 1.166666667 + 0.2222222222x + x2 = 0 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + 0.2222222222x + x2 = 0 + 1.166666667 0.2222222222x + x2 = 0 + 1.166666667 Combine like terms: 0 + 1.166666667 = 1.166666667 0.2222222222x + x2 = 1.166666667 The x term is 0.2222222222x. Take half its coefficient (0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. 0.2222222222x + 0.01234567901 + x2 = 1.166666667 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222x + x2 = 1.166666667 + 0.01234567901 Combine like terms: 1.166666667 + 0.01234567901 = 1.17901234601 0.01234567901 + 0.2222222222x + x2 = 1.17901234601 Factor a perfect square on the left side: (x + 0.1111111111)(x + 0.1111111111) = 1.17901234601 Calculate the square root of the right side: 1.085823349 Break this problem into two subproblems by setting (x + 0.1111111111) equal to 1.085823349 and -1.085823349.Subproblem 1
x + 0.1111111111 = 1.085823349 Simplifying x + 0.1111111111 = 1.085823349 Reorder the terms: 0.1111111111 + x = 1.085823349 Solving 0.1111111111 + x = 1.085823349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + x = 1.085823349 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = 1.085823349 + -0.1111111111 x = 1.085823349 + -0.1111111111 Combine like terms: 1.085823349 + -0.1111111111 = 0.9747122379 x = 0.9747122379 Simplifying x = 0.9747122379Subproblem 2
x + 0.1111111111 = -1.085823349 Simplifying x + 0.1111111111 = -1.085823349 Reorder the terms: 0.1111111111 + x = -1.085823349 Solving 0.1111111111 + x = -1.085823349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + x = -1.085823349 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = -1.085823349 + -0.1111111111 x = -1.085823349 + -0.1111111111 Combine like terms: -1.085823349 + -0.1111111111 = -1.1969344601 x = -1.1969344601 Simplifying x = -1.1969344601Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9747122379, -1.1969344601}
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