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Simplifying x2 + -9x = 96 Reorder the terms: -9x + x2 = 96 Solving -9x + x2 = 96 Solving for variable 'x'. Reorder the terms: -96 + -9x + x2 = 96 + -96 Combine like terms: 96 + -96 = 0 -96 + -9x + x2 = 0 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 = 15.281929326 x = 15.281929326 Simplifying x = 15.281929326Subproblem 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 = -6.281929326 x = -6.281929326 Simplifying x = -6.281929326Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.281929326, -6.281929326}
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