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Simplifying x2 + 4.5x + 5.1 = 14.1 Reorder the terms: 5.1 + 4.5x + x2 = 14.1 Solving 5.1 + 4.5x + x2 = 14.1 Solving for variable 'x'. Reorder the terms: 5.1 + -14.1 + 4.5x + x2 = 14.1 + -14.1 Combine like terms: 5.1 + -14.1 = -9 -9 + 4.5x + x2 = 14.1 + -14.1 Combine like terms: 14.1 + -14.1 = 0.0 -9 + 4.5x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 4.5x + 9 + x2 = 0.0 + 9 Reorder the terms: -9 + 9 + 4.5x + x2 = 0.0 + 9 Combine like terms: -9 + 9 = 0 0 + 4.5x + x2 = 0.0 + 9 4.5x + x2 = 0.0 + 9 Combine like terms: 0.0 + 9 = 9 4.5x + x2 = 9 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 = 9 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 9 + 5.0625 Combine like terms: 9 + 5.0625 = 14.0625 5.0625 + 4.5x + x2 = 14.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 14.0625 Calculate the square root of the right side: 3.75 Break this problem into two subproblems by setting (x + 2.25) equal to 3.75 and -3.75.Subproblem 1
x + 2.25 = 3.75 Simplifying x + 2.25 = 3.75 Reorder the terms: 2.25 + x = 3.75 Solving 2.25 + x = 3.75 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 = 3.75 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 3.75 + -2.25 x = 3.75 + -2.25 Combine like terms: 3.75 + -2.25 = 1.5 x = 1.5 Simplifying x = 1.5Subproblem 2
x + 2.25 = -3.75 Simplifying x + 2.25 = -3.75 Reorder the terms: 2.25 + x = -3.75 Solving 2.25 + x = -3.75 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 = -3.75 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -3.75 + -2.25 x = -3.75 + -2.25 Combine like terms: -3.75 + -2.25 = -6 x = -6 Simplifying x = -6Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5, -6}
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