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Simplifying -23.6 + 24x + -4x2 = 0 Solving -23.6 + 24x + -4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 5.9 + -6x + x2 = 0 Move the constant term to the right: Add '-5.9' to each side of the equation. 5.9 + -6x + -5.9 + x2 = 0 + -5.9 Reorder the terms: 5.9 + -5.9 + -6x + x2 = 0 + -5.9 Combine like terms: 5.9 + -5.9 = 0.0 0.0 + -6x + x2 = 0 + -5.9 -6x + x2 = 0 + -5.9 Combine like terms: 0 + -5.9 = -5.9 -6x + x2 = -5.9 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -5.9 + 9 Reorder the terms: 9 + -6x + x2 = -5.9 + 9 Combine like terms: -5.9 + 9 = 3.1 9 + -6x + x2 = 3.1 Factor a perfect square on the left side: (x + -3)(x + -3) = 3.1 Calculate the square root of the right side: 1.760681686 Break this problem into two subproblems by setting (x + -3) equal to 1.760681686 and -1.760681686.Subproblem 1
x + -3 = 1.760681686 Simplifying x + -3 = 1.760681686 Reorder the terms: -3 + x = 1.760681686 Solving -3 + x = 1.760681686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 1.760681686 + 3 Combine like terms: -3 + 3 = 0 0 + x = 1.760681686 + 3 x = 1.760681686 + 3 Combine like terms: 1.760681686 + 3 = 4.760681686 x = 4.760681686 Simplifying x = 4.760681686Subproblem 2
x + -3 = -1.760681686 Simplifying x + -3 = -1.760681686 Reorder the terms: -3 + x = -1.760681686 Solving -3 + x = -1.760681686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -1.760681686 + 3 Combine like terms: -3 + 3 = 0 0 + x = -1.760681686 + 3 x = -1.760681686 + 3 Combine like terms: -1.760681686 + 3 = 1.239318314 x = 1.239318314 Simplifying x = 1.239318314Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.760681686, 1.239318314}
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