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Simplifying x2 + (2x + 2)(2x + 2) = 13 Reorder the terms: x2 + (2 + 2x)(2x + 2) = 13 Reorder the terms: x2 + (2 + 2x)(2 + 2x) = 13 Multiply (2 + 2x) * (2 + 2x) x2 + (2(2 + 2x) + 2x * (2 + 2x)) = 13 x2 + ((2 * 2 + 2x * 2) + 2x * (2 + 2x)) = 13 x2 + ((4 + 4x) + 2x * (2 + 2x)) = 13 x2 + (4 + 4x + (2 * 2x + 2x * 2x)) = 13 x2 + (4 + 4x + (4x + 4x2)) = 13 Combine like terms: 4x + 4x = 8x x2 + (4 + 8x + 4x2) = 13 Reorder the terms: 4 + 8x + x2 + 4x2 = 13 Combine like terms: x2 + 4x2 = 5x2 4 + 8x + 5x2 = 13 Solving 4 + 8x + 5x2 = 13 Solving for variable 'x'. Reorder the terms: 4 + -13 + 8x + 5x2 = 13 + -13 Combine like terms: 4 + -13 = -9 -9 + 8x + 5x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -9 + 8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.8 + 1.6x + x2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 1.6x + 1.8 + x2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + 1.6x + x2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 1.6x + x2 = 0 + 1.8 1.6x + x2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 1.6x + x2 = 1.8 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = 1.8 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 1.8 + 0.64 Combine like terms: 1.8 + 0.64 = 2.44 0.64 + 1.6x + x2 = 2.44 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 2.44 Calculate the square root of the right side: 1.562049935 Break this problem into two subproblems by setting (x + 0.8) equal to 1.562049935 and -1.562049935.Subproblem 1
x + 0.8 = 1.562049935 Simplifying x + 0.8 = 1.562049935 Reorder the terms: 0.8 + x = 1.562049935 Solving 0.8 + x = 1.562049935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 1.562049935 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 1.562049935 + -0.8 x = 1.562049935 + -0.8 Combine like terms: 1.562049935 + -0.8 = 0.762049935 x = 0.762049935 Simplifying x = 0.762049935Subproblem 2
x + 0.8 = -1.562049935 Simplifying x + 0.8 = -1.562049935 Reorder the terms: 0.8 + x = -1.562049935 Solving 0.8 + x = -1.562049935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -1.562049935 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -1.562049935 + -0.8 x = -1.562049935 + -0.8 Combine like terms: -1.562049935 + -0.8 = -2.362049935 x = -2.362049935 Simplifying x = -2.362049935Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.762049935, -2.362049935}
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