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Simplifying x2 + 9x + -96 = 0 Reorder the terms: -96 + 9x + x2 = 0 Solving -96 + 9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '96' to each side of the equation. -96 + 9x + 96 + x2 = 0 + 96 Reorder the terms: -96 + 96 + 9x + x2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + 9x + x2 = 0 + 96 9x + x2 = 0 + 96 Combine like terms: 0 + 96 = 96 9x + x2 = 96 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 96 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 96 + 20.25 Combine like terms: 96 + 20.25 = 116.25 20.25 + 9x + x2 = 116.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 116.25 Calculate the square root of the right side: 10.781929326 Break this problem into two subproblems by setting (x + 4.5) equal to 10.781929326 and -10.781929326.Subproblem 1
x + 4.5 = 10.781929326 Simplifying x + 4.5 = 10.781929326 Reorder the terms: 4.5 + x = 10.781929326 Solving 4.5 + x = 10.781929326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 10.781929326 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 10.781929326 + -4.5 x = 10.781929326 + -4.5 Combine like terms: 10.781929326 + -4.5 = 6.281929326 x = 6.281929326 Simplifying x = 6.281929326Subproblem 2
x + 4.5 = -10.781929326 Simplifying x + 4.5 = -10.781929326 Reorder the terms: 4.5 + x = -10.781929326 Solving 4.5 + x = -10.781929326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -10.781929326 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -10.781929326 + -4.5 x = -10.781929326 + -4.5 Combine like terms: -10.781929326 + -4.5 = -15.281929326 x = -15.281929326 Simplifying x = -15.281929326Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.281929326, -15.281929326}
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