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Simplifying 2.25x + x2 = 2.25 Solving 2.25x + x2 = 2.25 Solving for variable 'x'. Reorder the terms: -2.25 + 2.25x + x2 = 2.25 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 -2.25 + 2.25x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 2.25x + 2.25 + x2 = 0.00 + 2.25 Reorder the terms: -2.25 + 2.25 + 2.25x + x2 = 0.00 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 2.25x + x2 = 0.00 + 2.25 2.25x + x2 = 0.00 + 2.25 Combine like terms: 0.00 + 2.25 = 2.25 2.25x + x2 = 2.25 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = 2.25 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 2.25 + 1.265625 Combine like terms: 2.25 + 1.265625 = 3.515625 1.265625 + 2.25x + x2 = 3.515625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 3.515625 Calculate the square root of the right side: 1.875 Break this problem into two subproblems by setting (x + 1.125) equal to 1.875 and -1.875.Subproblem 1
x + 1.125 = 1.875 Simplifying x + 1.125 = 1.875 Reorder the terms: 1.125 + x = 1.875 Solving 1.125 + x = 1.875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 1.875 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 1.875 + -1.125 x = 1.875 + -1.125 Combine like terms: 1.875 + -1.125 = 0.75 x = 0.75 Simplifying x = 0.75Subproblem 2
x + 1.125 = -1.875 Simplifying x + 1.125 = -1.875 Reorder the terms: 1.125 + x = -1.875 Solving 1.125 + x = -1.875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -1.875 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -1.875 + -1.125 x = -1.875 + -1.125 Combine like terms: -1.875 + -1.125 = -3 x = -3 Simplifying x = -3Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.75, -3}
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