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Simplifying x2 + -15x + (56.25) = 74.25 x2 + -15x + 56.25 = 74.25 Reorder the terms: 56.25 + -15x + x2 = 74.25 Solving 56.25 + -15x + x2 = 74.25 Solving for variable 'x'. Reorder the terms: 56.25 + -74.25 + -15x + x2 = 74.25 + -74.25 Combine like terms: 56.25 + -74.25 = -18 -18 + -15x + x2 = 74.25 + -74.25 Combine like terms: 74.25 + -74.25 = 0.00 -18 + -15x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -15x + 18 + x2 = 0.00 + 18 Reorder the terms: -18 + 18 + -15x + x2 = 0.00 + 18 Combine like terms: -18 + 18 = 0 0 + -15x + x2 = 0.00 + 18 -15x + x2 = 0.00 + 18 Combine like terms: 0.00 + 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 = 16.11684397 x = 16.11684397 Simplifying x = 16.11684397Subproblem 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 = -1.11684397 x = -1.11684397 Simplifying x = -1.11684397Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.11684397, -1.11684397}
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