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Simplifying 24x2 + -18x + 1 = 0 Reorder the terms: 1 + -18x + 24x2 = 0 Solving 1 + -18x + 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 + -0.75x + x2 = 0 Move the constant term to the right: Add '-0.04166666667' to each side of the equation. 0.04166666667 + -0.75x + -0.04166666667 + x2 = 0 + -0.04166666667 Reorder the terms: 0.04166666667 + -0.04166666667 + -0.75x + x2 = 0 + -0.04166666667 Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000 0.00000000000 + -0.75x + x2 = 0 + -0.04166666667 -0.75x + x2 = 0 + -0.04166666667 Combine like terms: 0 + -0.04166666667 = -0.04166666667 -0.75x + x2 = -0.04166666667 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = -0.04166666667 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = -0.04166666667 + 0.140625 Combine like terms: -0.04166666667 + 0.140625 = 0.09895833333 0.140625 + -0.75x + x2 = 0.09895833333 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 0.09895833333 Calculate the square root of the right side: 0.314576435 Break this problem into two subproblems by setting (x + -0.375) equal to 0.314576435 and -0.314576435.Subproblem 1
x + -0.375 = 0.314576435 Simplifying x + -0.375 = 0.314576435 Reorder the terms: -0.375 + x = 0.314576435 Solving -0.375 + x = 0.314576435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 0.314576435 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 0.314576435 + 0.375 x = 0.314576435 + 0.375 Combine like terms: 0.314576435 + 0.375 = 0.689576435 x = 0.689576435 Simplifying x = 0.689576435Subproblem 2
x + -0.375 = -0.314576435 Simplifying x + -0.375 = -0.314576435 Reorder the terms: -0.375 + x = -0.314576435 Solving -0.375 + x = -0.314576435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -0.314576435 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -0.314576435 + 0.375 x = -0.314576435 + 0.375 Combine like terms: -0.314576435 + 0.375 = 0.060423565 x = 0.060423565 Simplifying x = 0.060423565Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.689576435, 0.060423565}
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