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Simplifying x2 + 2x = 10.24 Reorder the terms: 2x + x2 = 10.24 Solving 2x + x2 = 10.24 Solving for variable 'x'. Reorder the terms: -10.24 + 2x + x2 = 10.24 + -10.24 Combine like terms: 10.24 + -10.24 = 0.00 -10.24 + 2x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '10.24' to each side of the equation. -10.24 + 2x + 10.24 + x2 = 0.00 + 10.24 Reorder the terms: -10.24 + 10.24 + 2x + x2 = 0.00 + 10.24 Combine like terms: -10.24 + 10.24 = 0.00 0.00 + 2x + x2 = 0.00 + 10.24 2x + x2 = 0.00 + 10.24 Combine like terms: 0.00 + 10.24 = 10.24 2x + x2 = 10.24 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 = 10.24 + 1 Reorder the terms: 1 + 2x + x2 = 10.24 + 1 Combine like terms: 10.24 + 1 = 11.24 1 + 2x + x2 = 11.24 Factor a perfect square on the left side: (x + 1)(x + 1) = 11.24 Calculate the square root of the right side: 3.352610923 Break this problem into two subproblems by setting (x + 1) equal to 3.352610923 and -3.352610923.Subproblem 1
x + 1 = 3.352610923 Simplifying x + 1 = 3.352610923 Reorder the terms: 1 + x = 3.352610923 Solving 1 + x = 3.352610923 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 = 3.352610923 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.352610923 + -1 x = 3.352610923 + -1 Combine like terms: 3.352610923 + -1 = 2.352610923 x = 2.352610923 Simplifying x = 2.352610923Subproblem 2
x + 1 = -3.352610923 Simplifying x + 1 = -3.352610923 Reorder the terms: 1 + x = -3.352610923 Solving 1 + x = -3.352610923 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 = -3.352610923 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.352610923 + -1 x = -3.352610923 + -1 Combine like terms: -3.352610923 + -1 = -4.352610923 x = -4.352610923 Simplifying x = -4.352610923Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.352610923, -4.352610923}
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