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Simplifying x2 + x = 35678 Reorder the terms: x + x2 = 35678 Solving x + x2 = 35678 Solving for variable 'x'. Reorder the terms: -35678 + x + x2 = 35678 + -35678 Combine like terms: 35678 + -35678 = 0 -35678 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '35678' to each side of the equation. -35678 + x + 35678 + x2 = 0 + 35678 Reorder the terms: -35678 + 35678 + x + x2 = 0 + 35678 Combine like terms: -35678 + 35678 = 0 0 + x + x2 = 0 + 35678 x + x2 = 0 + 35678 Combine like terms: 0 + 35678 = 35678 x + x2 = 35678 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 = 35678 + 0.25 Reorder the terms: 0.25 + x + x2 = 35678 + 0.25 Combine like terms: 35678 + 0.25 = 35678.25 0.25 + x + x2 = 35678.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 35678.25 Calculate the square root of the right side: 188.886870904 Break this problem into two subproblems by setting (x + 0.5) equal to 188.886870904 and -188.886870904.Subproblem 1
x + 0.5 = 188.886870904 Simplifying x + 0.5 = 188.886870904 Reorder the terms: 0.5 + x = 188.886870904 Solving 0.5 + x = 188.886870904 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 = 188.886870904 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 188.886870904 + -0.5 x = 188.886870904 + -0.5 Combine like terms: 188.886870904 + -0.5 = 188.386870904 x = 188.386870904 Simplifying x = 188.386870904Subproblem 2
x + 0.5 = -188.886870904 Simplifying x + 0.5 = -188.886870904 Reorder the terms: 0.5 + x = -188.886870904 Solving 0.5 + x = -188.886870904 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 = -188.886870904 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -188.886870904 + -0.5 x = -188.886870904 + -0.5 Combine like terms: -188.886870904 + -0.5 = -189.386870904 x = -189.386870904 Simplifying x = -189.386870904Solution
The solution to the problem is based on the solutions from the subproblems. x = {188.386870904, -189.386870904}
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