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Simplifying x(x + -17) = 44 Reorder the terms: x(-17 + x) = 44 (-17 * x + x * x) = 44 (-17x + x2) = 44 Solving -17x + x2 = 44 Solving for variable 'x'. Reorder the terms: -44 + -17x + x2 = 44 + -44 Combine like terms: 44 + -44 = 0 -44 + -17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + -17x + 44 + x2 = 0 + 44 Reorder the terms: -44 + 44 + -17x + x2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + -17x + x2 = 0 + 44 -17x + x2 = 0 + 44 Combine like terms: 0 + 44 = 44 -17x + x2 = 44 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = 44 + 72.25 Reorder the terms: 72.25 + -17x + x2 = 44 + 72.25 Combine like terms: 44 + 72.25 = 116.25 72.25 + -17x + x2 = 116.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 116.25 Calculate the square root of the right side: 10.781929326 Break this problem into two subproblems by setting (x + -8.5) equal to 10.781929326 and -10.781929326.Subproblem 1
x + -8.5 = 10.781929326 Simplifying x + -8.5 = 10.781929326 Reorder the terms: -8.5 + x = 10.781929326 Solving -8.5 + x = 10.781929326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 10.781929326 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 10.781929326 + 8.5 x = 10.781929326 + 8.5 Combine like terms: 10.781929326 + 8.5 = 19.281929326 x = 19.281929326 Simplifying x = 19.281929326Subproblem 2
x + -8.5 = -10.781929326 Simplifying x + -8.5 = -10.781929326 Reorder the terms: -8.5 + x = -10.781929326 Solving -8.5 + x = -10.781929326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -10.781929326 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -10.781929326 + 8.5 x = -10.781929326 + 8.5 Combine like terms: -10.781929326 + 8.5 = -2.281929326 x = -2.281929326 Simplifying x = -2.281929326Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.281929326, -2.281929326}
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