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Simplifying x2 + -5x = 9 Reorder the terms: -5x + x2 = 9 Solving -5x + x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + -5x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -5x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -5x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -5x + x2 = 0 + 9 -5x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -5x + x2 = 9 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 9 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 9 + 6.25 Combine like terms: 9 + 6.25 = 15.25 6.25 + -5x + x2 = 15.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (x + -2.5) equal to 3.905124838 and -3.905124838.Subproblem 1
x + -2.5 = 3.905124838 Simplifying x + -2.5 = 3.905124838 Reorder the terms: -2.5 + x = 3.905124838 Solving -2.5 + x = 3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 3.905124838 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.905124838 + 2.5 x = 3.905124838 + 2.5 Combine like terms: 3.905124838 + 2.5 = 6.405124838 x = 6.405124838 Simplifying x = 6.405124838Subproblem 2
x + -2.5 = -3.905124838 Simplifying x + -2.5 = -3.905124838 Reorder the terms: -2.5 + x = -3.905124838 Solving -2.5 + x = -3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -3.905124838 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.905124838 + 2.5 x = -3.905124838 + 2.5 Combine like terms: -3.905124838 + 2.5 = -1.405124838 x = -1.405124838 Simplifying x = -1.405124838Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.405124838, -1.405124838}
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