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Simplifying x(x + -13) = 22 Reorder the terms: x(-13 + x) = 22 (-13 * x + x * x) = 22 (-13x + x2) = 22 Solving -13x + x2 = 22 Solving for variable 'x'. Reorder the terms: -22 + -13x + x2 = 22 + -22 Combine like terms: 22 + -22 = 0 -22 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + -13x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + -13x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -13x + x2 = 0 + 22 -13x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 -13x + x2 = 22 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = 22 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 22 + 42.25 Combine like terms: 22 + 42.25 = 64.25 42.25 + -13x + x2 = 64.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 64.25 Calculate the square root of the right side: 8.015609771 Break this problem into two subproblems by setting (x + -6.5) equal to 8.015609771 and -8.015609771.Subproblem 1
x + -6.5 = 8.015609771 Simplifying x + -6.5 = 8.015609771 Reorder the terms: -6.5 + x = 8.015609771 Solving -6.5 + x = 8.015609771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 8.015609771 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 8.015609771 + 6.5 x = 8.015609771 + 6.5 Combine like terms: 8.015609771 + 6.5 = 14.515609771 x = 14.515609771 Simplifying x = 14.515609771Subproblem 2
x + -6.5 = -8.015609771 Simplifying x + -6.5 = -8.015609771 Reorder the terms: -6.5 + x = -8.015609771 Solving -6.5 + x = -8.015609771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -8.015609771 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -8.015609771 + 6.5 x = -8.015609771 + 6.5 Combine like terms: -8.015609771 + 6.5 = -1.515609771 x = -1.515609771 Simplifying x = -1.515609771Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.515609771, -1.515609771}
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