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Simplifying x2 + 4.5x = 28 Reorder the terms: 4.5x + x2 = 28 Solving 4.5x + x2 = 28 Solving for variable 'x'. Reorder the terms: -28 + 4.5x + x2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + 4.5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + 4.5x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + 4.5x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 4.5x + x2 = 0 + 28 4.5x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 4.5x + x2 = 28 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 28 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 28 + 5.0625 Combine like terms: 28 + 5.0625 = 33.0625 5.0625 + 4.5x + x2 = 33.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 33.0625 Calculate the square root of the right side: 5.75 Break this problem into two subproblems by setting (x + 2.25) equal to 5.75 and -5.75.Subproblem 1
x + 2.25 = 5.75 Simplifying x + 2.25 = 5.75 Reorder the terms: 2.25 + x = 5.75 Solving 2.25 + x = 5.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 5.75 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 5.75 + -2.25 x = 5.75 + -2.25 Combine like terms: 5.75 + -2.25 = 3.5 x = 3.5 Simplifying x = 3.5Subproblem 2
x + 2.25 = -5.75 Simplifying x + 2.25 = -5.75 Reorder the terms: 2.25 + x = -5.75 Solving 2.25 + x = -5.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -5.75 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -5.75 + -2.25 x = -5.75 + -2.25 Combine like terms: -5.75 + -2.25 = -8 x = -8 Simplifying x = -8Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.5, -8}
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