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Simplifying x2 + 2x + -9.24 = 0 Reorder the terms: -9.24 + 2x + x2 = 0 Solving -9.24 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '9.24' to each side of the equation. -9.24 + 2x + 9.24 + x2 = 0 + 9.24 Reorder the terms: -9.24 + 9.24 + 2x + x2 = 0 + 9.24 Combine like terms: -9.24 + 9.24 = 0.00 0.00 + 2x + x2 = 0 + 9.24 2x + x2 = 0 + 9.24 Combine like terms: 0 + 9.24 = 9.24 2x + x2 = 9.24 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 = 9.24 + 1 Reorder the terms: 1 + 2x + x2 = 9.24 + 1 Combine like terms: 9.24 + 1 = 10.24 1 + 2x + x2 = 10.24 Factor a perfect square on the left side: (x + 1)(x + 1) = 10.24 Calculate the square root of the right side: 3.2 Break this problem into two subproblems by setting (x + 1) equal to 3.2 and -3.2.Subproblem 1
x + 1 = 3.2 Simplifying x + 1 = 3.2 Reorder the terms: 1 + x = 3.2 Solving 1 + x = 3.2 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 = 3.2 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.2 + -1 x = 3.2 + -1 Combine like terms: 3.2 + -1 = 2.2 x = 2.2 Simplifying x = 2.2Subproblem 2
x + 1 = -3.2 Simplifying x + 1 = -3.2 Reorder the terms: 1 + x = -3.2 Solving 1 + x = -3.2 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 = -3.2 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.2 + -1 x = -3.2 + -1 Combine like terms: -3.2 + -1 = -4.2 x = -4.2 Simplifying x = -4.2Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2, -4.2}
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