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Simplifying x(x + 1) = 74 Reorder the terms: x(1 + x) = 74 (1 * x + x * x) = 74 (1x + x2) = 74 Solving 1x + x2 = 74 Solving for variable 'x'. Reorder the terms: -74 + 1x + x2 = 74 + -74 Combine like terms: 74 + -74 = 0 -74 + 1x + x2 = 0 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. x + 0.25 + x2 = 74 + 0.25 Reorder the terms: 0.25 + x + x2 = 74 + 0.25 Combine like terms: 74 + 0.25 = 74.25 0.25 + x + 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 = 8.11684397 x = 8.11684397 Simplifying x = 8.11684397Subproblem 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 = -9.11684397 x = -9.11684397 Simplifying x = -9.11684397Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.11684397, -9.11684397}
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