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Simplifying 24x2 + -3x = 68 Reorder the terms: -3x + 24x2 = 68 Solving -3x + 24x2 = 68 Solving for variable 'x'. Reorder the terms: -68 + -3x + 24x2 = 68 + -68 Combine like terms: 68 + -68 = 0 -68 + -3x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -2.833333333 + -0.125x + x2 = 0 Move the constant term to the right: Add '2.833333333' to each side of the equation. -2.833333333 + -0.125x + 2.833333333 + x2 = 0 + 2.833333333 Reorder the terms: -2.833333333 + 2.833333333 + -0.125x + x2 = 0 + 2.833333333 Combine like terms: -2.833333333 + 2.833333333 = 0.000000000 0.000000000 + -0.125x + x2 = 0 + 2.833333333 -0.125x + x2 = 0 + 2.833333333 Combine like terms: 0 + 2.833333333 = 2.833333333 -0.125x + x2 = 2.833333333 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 = 2.833333333 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x + x2 = 2.833333333 + 0.00390625 Combine like terms: 2.833333333 + 0.00390625 = 2.837239583 0.00390625 + -0.125x + x2 = 2.837239583 Factor a perfect square on the left side: (x + -0.0625)(x + -0.0625) = 2.837239583 Calculate the square root of the right side: 1.684410752 Break this problem into two subproblems by setting (x + -0.0625) equal to 1.684410752 and -1.684410752.Subproblem 1
x + -0.0625 = 1.684410752 Simplifying x + -0.0625 = 1.684410752 Reorder the terms: -0.0625 + x = 1.684410752 Solving -0.0625 + x = 1.684410752 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 = 1.684410752 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 1.684410752 + 0.0625 x = 1.684410752 + 0.0625 Combine like terms: 1.684410752 + 0.0625 = 1.746910752 x = 1.746910752 Simplifying x = 1.746910752Subproblem 2
x + -0.0625 = -1.684410752 Simplifying x + -0.0625 = -1.684410752 Reorder the terms: -0.0625 + x = -1.684410752 Solving -0.0625 + x = -1.684410752 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 = -1.684410752 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -1.684410752 + 0.0625 x = -1.684410752 + 0.0625 Combine like terms: -1.684410752 + 0.0625 = -1.621910752 x = -1.621910752 Simplifying x = -1.621910752Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.746910752, -1.621910752}
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