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Simplifying x2 + -1x + -74 = 0 Reorder the terms: -74 + -1x + x2 = 0 Solving -74 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '74' to each side of the equation. -74 + -1x + 74 + x2 = 0 + 74 Reorder the terms: -74 + 74 + -1x + x2 = 0 + 74 Combine like terms: -74 + 74 = 0 0 + -1x + x2 = 0 + 74 -1x + x2 = 0 + 74 Combine like terms: 0 + 74 = 74 -1x + x2 = 74 The x term is -1x. 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. -1x + 0.25 + x2 = 74 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 74 + 0.25 Combine like terms: 74 + 0.25 = 74.25 0.25 + -1x + x2 = 74.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 74.25 Calculate the square root of the right side: 8.61684397 Break this problem into two subproblems by setting (x + -0.5) equal to 8.61684397 and -8.61684397.Subproblem 1
x + -0.5 = 8.61684397 Simplifying x + -0.5 = 8.61684397 Reorder the terms: -0.5 + x = 8.61684397 Solving -0.5 + x = 8.61684397 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 = 8.61684397 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 8.61684397 + 0.5 x = 8.61684397 + 0.5 Combine like terms: 8.61684397 + 0.5 = 9.11684397 x = 9.11684397 Simplifying x = 9.11684397Subproblem 2
x + -0.5 = -8.61684397 Simplifying x + -0.5 = -8.61684397 Reorder the terms: -0.5 + x = -8.61684397 Solving -0.5 + x = -8.61684397 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 = -8.61684397 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -8.61684397 + 0.5 x = -8.61684397 + 0.5 Combine like terms: -8.61684397 + 0.5 = -8.11684397 x = -8.11684397 Simplifying x = -8.11684397Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.11684397, -8.11684397}
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