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Simplifying x2 + -5x + -164 = 0 Reorder the terms: -164 + -5x + x2 = 0 Solving -164 + -5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '164' to each side of the equation. -164 + -5x + 164 + x2 = 0 + 164 Reorder the terms: -164 + 164 + -5x + x2 = 0 + 164 Combine like terms: -164 + 164 = 0 0 + -5x + x2 = 0 + 164 -5x + x2 = 0 + 164 Combine like terms: 0 + 164 = 164 -5x + x2 = 164 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 = 164 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 164 + 6.25 Combine like terms: 164 + 6.25 = 170.25 6.25 + -5x + x2 = 170.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 170.25 Calculate the square root of the right side: 13.047988351 Break this problem into two subproblems by setting (x + -2.5) equal to 13.047988351 and -13.047988351.Subproblem 1
x + -2.5 = 13.047988351 Simplifying x + -2.5 = 13.047988351 Reorder the terms: -2.5 + x = 13.047988351 Solving -2.5 + x = 13.047988351 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 = 13.047988351 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 13.047988351 + 2.5 x = 13.047988351 + 2.5 Combine like terms: 13.047988351 + 2.5 = 15.547988351 x = 15.547988351 Simplifying x = 15.547988351Subproblem 2
x + -2.5 = -13.047988351 Simplifying x + -2.5 = -13.047988351 Reorder the terms: -2.5 + x = -13.047988351 Solving -2.5 + x = -13.047988351 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 = -13.047988351 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -13.047988351 + 2.5 x = -13.047988351 + 2.5 Combine like terms: -13.047988351 + 2.5 = -10.547988351 x = -10.547988351 Simplifying x = -10.547988351Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.547988351, -10.547988351}
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