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Simplifying x * x + 2x + -19.25 = 0 Multiply x * x x2 + 2x + -19.25 = 0 Reorder the terms: -19.25 + 2x + x2 = 0 Solving -19.25 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '19.25' to each side of the equation. -19.25 + 2x + 19.25 + x2 = 0 + 19.25 Reorder the terms: -19.25 + 19.25 + 2x + x2 = 0 + 19.25 Combine like terms: -19.25 + 19.25 = 0.00 0.00 + 2x + x2 = 0 + 19.25 2x + x2 = 0 + 19.25 Combine like terms: 0 + 19.25 = 19.25 2x + x2 = 19.25 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 19.25 + 1 Reorder the terms: 1 + 2x + x2 = 19.25 + 1 Combine like terms: 19.25 + 1 = 20.25 1 + 2x + x2 = 20.25 Factor a perfect square on the left side: (x + 1)(x + 1) = 20.25 Calculate the square root of the right side: 4.5 Break this problem into two subproblems by setting (x + 1) equal to 4.5 and -4.5.Subproblem 1
x + 1 = 4.5 Simplifying x + 1 = 4.5 Reorder the terms: 1 + x = 4.5 Solving 1 + x = 4.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 4.5 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.5 + -1 x = 4.5 + -1 Combine like terms: 4.5 + -1 = 3.5 x = 3.5 Simplifying x = 3.5Subproblem 2
x + 1 = -4.5 Simplifying x + 1 = -4.5 Reorder the terms: 1 + x = -4.5 Solving 1 + x = -4.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -4.5 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.5 + -1 x = -4.5 + -1 Combine like terms: -4.5 + -1 = -5.5 x = -5.5 Simplifying x = -5.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.5, -5.5}
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