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Simplifying 24x2 + 3x + -2 = 0 Reorder the terms: -2 + 3x + 24x2 = 0 Solving -2 + 3x + 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'. -0.08333333333 + 0.125x + x2 = 0 Move the constant term to the right: Add '0.08333333333' to each side of the equation. -0.08333333333 + 0.125x + 0.08333333333 + x2 = 0 + 0.08333333333 Reorder the terms: -0.08333333333 + 0.08333333333 + 0.125x + x2 = 0 + 0.08333333333 Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000 0.00000000000 + 0.125x + x2 = 0 + 0.08333333333 0.125x + x2 = 0 + 0.08333333333 Combine like terms: 0 + 0.08333333333 = 0.08333333333 0.125x + x2 = 0.08333333333 The x term is 0.125x. Take half its coefficient (0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. 0.125x + 0.00390625 + x2 = 0.08333333333 + 0.00390625 Reorder the terms: 0.00390625 + 0.125x + x2 = 0.08333333333 + 0.00390625 Combine like terms: 0.08333333333 + 0.00390625 = 0.08723958333 0.00390625 + 0.125x + x2 = 0.08723958333 Factor a perfect square on the left side: (x + 0.0625)(x + 0.0625) = 0.08723958333 Calculate the square root of the right side: 0.295363477 Break this problem into two subproblems by setting (x + 0.0625) equal to 0.295363477 and -0.295363477.Subproblem 1
x + 0.0625 = 0.295363477 Simplifying x + 0.0625 = 0.295363477 Reorder the terms: 0.0625 + x = 0.295363477 Solving 0.0625 + x = 0.295363477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + x = 0.295363477 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = 0.295363477 + -0.0625 x = 0.295363477 + -0.0625 Combine like terms: 0.295363477 + -0.0625 = 0.232863477 x = 0.232863477 Simplifying x = 0.232863477Subproblem 2
x + 0.0625 = -0.295363477 Simplifying x + 0.0625 = -0.295363477 Reorder the terms: 0.0625 + x = -0.295363477 Solving 0.0625 + x = -0.295363477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + x = -0.295363477 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = -0.295363477 + -0.0625 x = -0.295363477 + -0.0625 Combine like terms: -0.295363477 + -0.0625 = -0.357863477 x = -0.357863477 Simplifying x = -0.357863477Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.232863477, -0.357863477}
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