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Simplifying x2 + 9x + -3375 = 0 Reorder the terms: -3375 + 9x + x2 = 0 Solving -3375 + 9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3375' to each side of the equation. -3375 + 9x + 3375 + x2 = 0 + 3375 Reorder the terms: -3375 + 3375 + 9x + x2 = 0 + 3375 Combine like terms: -3375 + 3375 = 0 0 + 9x + x2 = 0 + 3375 9x + x2 = 0 + 3375 Combine like terms: 0 + 3375 = 3375 9x + x2 = 3375 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 3375 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 3375 + 20.25 Combine like terms: 3375 + 20.25 = 3395.25 20.25 + 9x + x2 = 3395.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 3395.25 Calculate the square root of the right side: 58.268773799 Break this problem into two subproblems by setting (x + 4.5) equal to 58.268773799 and -58.268773799.Subproblem 1
x + 4.5 = 58.268773799 Simplifying x + 4.5 = 58.268773799 Reorder the terms: 4.5 + x = 58.268773799 Solving 4.5 + x = 58.268773799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 58.268773799 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 58.268773799 + -4.5 x = 58.268773799 + -4.5 Combine like terms: 58.268773799 + -4.5 = 53.768773799 x = 53.768773799 Simplifying x = 53.768773799Subproblem 2
x + 4.5 = -58.268773799 Simplifying x + 4.5 = -58.268773799 Reorder the terms: 4.5 + x = -58.268773799 Solving 4.5 + x = -58.268773799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -58.268773799 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -58.268773799 + -4.5 x = -58.268773799 + -4.5 Combine like terms: -58.268773799 + -4.5 = -62.768773799 x = -62.768773799 Simplifying x = -62.768773799Solution
The solution to the problem is based on the solutions from the subproblems. x = {53.768773799, -62.768773799}
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