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Simplifying (x * x) + x = 170 Multiply x * x (x2) + x = 170 x2 + x = 170 Reorder the terms: x + x2 = 170 Solving x + x2 = 170 Solving for variable 'x'. Reorder the terms: -170 + x + x2 = 170 + -170 Combine like terms: 170 + -170 = 0 -170 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '170' to each side of the equation. -170 + x + 170 + x2 = 0 + 170 Reorder the terms: -170 + 170 + x + x2 = 0 + 170 Combine like terms: -170 + 170 = 0 0 + x + x2 = 0 + 170 x + x2 = 0 + 170 Combine like terms: 0 + 170 = 170 x + x2 = 170 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 170 + 0.25 Reorder the terms: 0.25 + x + x2 = 170 + 0.25 Combine like terms: 170 + 0.25 = 170.25 0.25 + x + x2 = 170.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 170.25 Calculate the square root of the right side: 13.047988351 Break this problem into two subproblems by setting (x + 0.5) equal to 13.047988351 and -13.047988351.Subproblem 1
x + 0.5 = 13.047988351 Simplifying x + 0.5 = 13.047988351 Reorder the terms: 0.5 + x = 13.047988351 Solving 0.5 + x = 13.047988351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 13.047988351 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 13.047988351 + -0.5 x = 13.047988351 + -0.5 Combine like terms: 13.047988351 + -0.5 = 12.547988351 x = 12.547988351 Simplifying x = 12.547988351Subproblem 2
x + 0.5 = -13.047988351 Simplifying x + 0.5 = -13.047988351 Reorder the terms: 0.5 + x = -13.047988351 Solving 0.5 + x = -13.047988351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -13.047988351 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -13.047988351 + -0.5 x = -13.047988351 + -0.5 Combine like terms: -13.047988351 + -0.5 = -13.547988351 x = -13.547988351 Simplifying x = -13.547988351Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.547988351, -13.547988351}
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