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Simplifying 24x2 + -27x + 1 = 0 Reorder the terms: 1 + -27x + 24x2 = 0 Solving 1 + -27x + 24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. 0.04166666667 + -1.125x + x2 = 0 Move the constant term to the right: Add '-0.04166666667' to each side of the equation. 0.04166666667 + -1.125x + -0.04166666667 + x2 = 0 + -0.04166666667 Reorder the terms: 0.04166666667 + -0.04166666667 + -1.125x + x2 = 0 + -0.04166666667 Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000 0.00000000000 + -1.125x + x2 = 0 + -0.04166666667 -1.125x + x2 = 0 + -0.04166666667 Combine like terms: 0 + -0.04166666667 = -0.04166666667 -1.125x + x2 = -0.04166666667 The x term is -1.125x. Take half its coefficient (-0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. -1.125x + 0.31640625 + x2 = -0.04166666667 + 0.31640625 Reorder the terms: 0.31640625 + -1.125x + x2 = -0.04166666667 + 0.31640625 Combine like terms: -0.04166666667 + 0.31640625 = 0.27473958333 0.31640625 + -1.125x + x2 = 0.27473958333 Factor a perfect square on the left side: (x + -0.5625)(x + -0.5625) = 0.27473958333 Calculate the square root of the right side: 0.524156068 Break this problem into two subproblems by setting (x + -0.5625) equal to 0.524156068 and -0.524156068.Subproblem 1
x + -0.5625 = 0.524156068 Simplifying x + -0.5625 = 0.524156068 Reorder the terms: -0.5625 + x = 0.524156068 Solving -0.5625 + x = 0.524156068 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = 0.524156068 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = 0.524156068 + 0.5625 x = 0.524156068 + 0.5625 Combine like terms: 0.524156068 + 0.5625 = 1.086656068 x = 1.086656068 Simplifying x = 1.086656068Subproblem 2
x + -0.5625 = -0.524156068 Simplifying x + -0.5625 = -0.524156068 Reorder the terms: -0.5625 + x = -0.524156068 Solving -0.5625 + x = -0.524156068 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = -0.524156068 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = -0.524156068 + 0.5625 x = -0.524156068 + 0.5625 Combine like terms: -0.524156068 + 0.5625 = 0.038343932 x = 0.038343932 Simplifying x = 0.038343932Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.086656068, 0.038343932}
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