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Simplifying x2 + 15x + -183.75 = 0 Reorder the terms: -183.75 + 15x + x2 = 0 Solving -183.75 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '183.75' to each side of the equation. -183.75 + 15x + 183.75 + x2 = 0 + 183.75 Reorder the terms: -183.75 + 183.75 + 15x + x2 = 0 + 183.75 Combine like terms: -183.75 + 183.75 = 0.00 0.00 + 15x + x2 = 0 + 183.75 15x + x2 = 0 + 183.75 Combine like terms: 0 + 183.75 = 183.75 15x + x2 = 183.75 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 = 183.75 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 183.75 + 56.25 Combine like terms: 183.75 + 56.25 = 240 56.25 + 15x + x2 = 240 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 240 Calculate the square root of the right side: 15.491933385 Break this problem into two subproblems by setting (x + 7.5) equal to 15.491933385 and -15.491933385.Subproblem 1
x + 7.5 = 15.491933385 Simplifying x + 7.5 = 15.491933385 Reorder the terms: 7.5 + x = 15.491933385 Solving 7.5 + x = 15.491933385 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 = 15.491933385 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 15.491933385 + -7.5 x = 15.491933385 + -7.5 Combine like terms: 15.491933385 + -7.5 = 7.991933385 x = 7.991933385 Simplifying x = 7.991933385Subproblem 2
x + 7.5 = -15.491933385 Simplifying x + 7.5 = -15.491933385 Reorder the terms: 7.5 + x = -15.491933385 Solving 7.5 + x = -15.491933385 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 = -15.491933385 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -15.491933385 + -7.5 x = -15.491933385 + -7.5 Combine like terms: -15.491933385 + -7.5 = -22.991933385 x = -22.991933385 Simplifying x = -22.991933385Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.991933385, -22.991933385}
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