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Simplifying 23x2 + -116x + -96 = 0 Reorder the terms: -96 + -116x + 23x2 = 0 Solving -96 + -116x + 23x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 23 the coefficient of the squared term: Divide each side by '23'. -4.173913043 + -5.043478261x + x2 = 0 Move the constant term to the right: Add '4.173913043' to each side of the equation. -4.173913043 + -5.043478261x + 4.173913043 + x2 = 0 + 4.173913043 Reorder the terms: -4.173913043 + 4.173913043 + -5.043478261x + x2 = 0 + 4.173913043 Combine like terms: -4.173913043 + 4.173913043 = 0.000000000 0.000000000 + -5.043478261x + x2 = 0 + 4.173913043 -5.043478261x + x2 = 0 + 4.173913043 Combine like terms: 0 + 4.173913043 = 4.173913043 -5.043478261x + x2 = 4.173913043 The x term is -5.043478261x. Take half its coefficient (-2.521739131). Square it (6.359168245) and add it to both sides. Add '6.359168245' to each side of the equation. -5.043478261x + 6.359168245 + x2 = 4.173913043 + 6.359168245 Reorder the terms: 6.359168245 + -5.043478261x + x2 = 4.173913043 + 6.359168245 Combine like terms: 4.173913043 + 6.359168245 = 10.533081288 6.359168245 + -5.043478261x + x2 = 10.533081288 Factor a perfect square on the left side: (x + -2.521739131)(x + -2.521739131) = 10.533081288 Calculate the square root of the right side: 3.245470888 Break this problem into two subproblems by setting (x + -2.521739131) equal to 3.245470888 and -3.245470888.Subproblem 1
x + -2.521739131 = 3.245470888 Simplifying x + -2.521739131 = 3.245470888 Reorder the terms: -2.521739131 + x = 3.245470888 Solving -2.521739131 + x = 3.245470888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.521739131' to each side of the equation. -2.521739131 + 2.521739131 + x = 3.245470888 + 2.521739131 Combine like terms: -2.521739131 + 2.521739131 = 0.000000000 0.000000000 + x = 3.245470888 + 2.521739131 x = 3.245470888 + 2.521739131 Combine like terms: 3.245470888 + 2.521739131 = 5.767210019 x = 5.767210019 Simplifying x = 5.767210019Subproblem 2
x + -2.521739131 = -3.245470888 Simplifying x + -2.521739131 = -3.245470888 Reorder the terms: -2.521739131 + x = -3.245470888 Solving -2.521739131 + x = -3.245470888 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.521739131' to each side of the equation. -2.521739131 + 2.521739131 + x = -3.245470888 + 2.521739131 Combine like terms: -2.521739131 + 2.521739131 = 0.000000000 0.000000000 + x = -3.245470888 + 2.521739131 x = -3.245470888 + 2.521739131 Combine like terms: -3.245470888 + 2.521739131 = -0.723731757 x = -0.723731757 Simplifying x = -0.723731757Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.767210019, -0.723731757}
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