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Simplifying x2 + 9x = 43.75 Reorder the terms: 9x + x2 = 43.75 Solving 9x + x2 = 43.75 Solving for variable 'x'. Reorder the terms: -43.75 + 9x + x2 = 43.75 + -43.75 Combine like terms: 43.75 + -43.75 = 0.00 -43.75 + 9x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '43.75' to each side of the equation. -43.75 + 9x + 43.75 + x2 = 0.00 + 43.75 Reorder the terms: -43.75 + 43.75 + 9x + x2 = 0.00 + 43.75 Combine like terms: -43.75 + 43.75 = 0.00 0.00 + 9x + x2 = 0.00 + 43.75 9x + x2 = 0.00 + 43.75 Combine like terms: 0.00 + 43.75 = 43.75 9x + x2 = 43.75 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 = 43.75 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 43.75 + 20.25 Combine like terms: 43.75 + 20.25 = 64 20.25 + 9x + x2 = 64 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 64 Calculate the square root of the right side: 8 Break this problem into two subproblems by setting (x + 4.5) equal to 8 and -8.Subproblem 1
x + 4.5 = 8 Simplifying x + 4.5 = 8 Reorder the terms: 4.5 + x = 8 Solving 4.5 + x = 8 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 = 8 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 8 + -4.5 x = 8 + -4.5 Combine like terms: 8 + -4.5 = 3.5 x = 3.5 Simplifying x = 3.5Subproblem 2
x + 4.5 = -8 Simplifying x + 4.5 = -8 Reorder the terms: 4.5 + x = -8 Solving 4.5 + x = -8 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 = -8 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -8 + -4.5 x = -8 + -4.5 Combine like terms: -8 + -4.5 = -12.5 x = -12.5 Simplifying x = -12.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.5, -12.5}
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