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Simplifying x2 + 15x = 18 Reorder the terms: 15x + x2 = 18 Solving 15x + x2 = 18 Solving for variable 'x'. Reorder the terms: -18 + 15x + x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 15x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 15x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 15x + x2 = 0 + 18 15x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 15x + x2 = 18 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 18 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 18 + 56.25 Combine like terms: 18 + 56.25 = 74.25 56.25 + 15x + x2 = 74.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 74.25 Calculate the square root of the right side: 8.61684397 Break this problem into two subproblems by setting (x + 7.5) equal to 8.61684397 and -8.61684397.Subproblem 1
x + 7.5 = 8.61684397 Simplifying x + 7.5 = 8.61684397 Reorder the terms: 7.5 + x = 8.61684397 Solving 7.5 + x = 8.61684397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 8.61684397 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 8.61684397 + -7.5 x = 8.61684397 + -7.5 Combine like terms: 8.61684397 + -7.5 = 1.11684397 x = 1.11684397 Simplifying x = 1.11684397Subproblem 2
x + 7.5 = -8.61684397 Simplifying x + 7.5 = -8.61684397 Reorder the terms: 7.5 + x = -8.61684397 Solving 7.5 + x = -8.61684397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -8.61684397 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -8.61684397 + -7.5 x = -8.61684397 + -7.5 Combine like terms: -8.61684397 + -7.5 = -16.11684397 x = -16.11684397 Simplifying x = -16.11684397Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.11684397, -16.11684397}
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