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Simplifying (3.39 + x)(2.14 + x) = 64 Multiply (3.39 + x) * (2.14 + x) (3.39(2.14 + x) + x(2.14 + x)) = 64 ((2.14 * 3.39 + x * 3.39) + x(2.14 + x)) = 64 ((7.2546 + 3.39x) + x(2.14 + x)) = 64 (7.2546 + 3.39x + (2.14 * x + x * x)) = 64 (7.2546 + 3.39x + (2.14x + x2)) = 64 Combine like terms: 3.39x + 2.14x = 5.53x (7.2546 + 5.53x + x2) = 64 Solving 7.2546 + 5.53x + x2 = 64 Solving for variable 'x'. Reorder the terms: 7.2546 + -64 + 5.53x + x2 = 64 + -64 Combine like terms: 7.2546 + -64 = -56.7454 -56.7454 + 5.53x + x2 = 64 + -64 Combine like terms: 64 + -64 = 0 -56.7454 + 5.53x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '56.7454' to each side of the equation. -56.7454 + 5.53x + 56.7454 + x2 = 0 + 56.7454 Reorder the terms: -56.7454 + 56.7454 + 5.53x + x2 = 0 + 56.7454 Combine like terms: -56.7454 + 56.7454 = 0.0000 0.0000 + 5.53x + x2 = 0 + 56.7454 5.53x + x2 = 0 + 56.7454 Combine like terms: 0 + 56.7454 = 56.7454 5.53x + x2 = 56.7454 The x term is 5.53x. Take half its coefficient (2.765). Square it (7.645225) and add it to both sides. Add '7.645225' to each side of the equation. 5.53x + 7.645225 + x2 = 56.7454 + 7.645225 Reorder the terms: 7.645225 + 5.53x + x2 = 56.7454 + 7.645225 Combine like terms: 56.7454 + 7.645225 = 64.390625 7.645225 + 5.53x + x2 = 64.390625 Factor a perfect square on the left side: (x + 2.765)(x + 2.765) = 64.390625 Calculate the square root of the right side: 8.024376923 Break this problem into two subproblems by setting (x + 2.765) equal to 8.024376923 and -8.024376923.Subproblem 1
x + 2.765 = 8.024376923 Simplifying x + 2.765 = 8.024376923 Reorder the terms: 2.765 + x = 8.024376923 Solving 2.765 + x = 8.024376923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.765' to each side of the equation. 2.765 + -2.765 + x = 8.024376923 + -2.765 Combine like terms: 2.765 + -2.765 = 0.000 0.000 + x = 8.024376923 + -2.765 x = 8.024376923 + -2.765 Combine like terms: 8.024376923 + -2.765 = 5.259376923 x = 5.259376923 Simplifying x = 5.259376923Subproblem 2
x + 2.765 = -8.024376923 Simplifying x + 2.765 = -8.024376923 Reorder the terms: 2.765 + x = -8.024376923 Solving 2.765 + x = -8.024376923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.765' to each side of the equation. 2.765 + -2.765 + x = -8.024376923 + -2.765 Combine like terms: 2.765 + -2.765 = 0.000 0.000 + x = -8.024376923 + -2.765 x = -8.024376923 + -2.765 Combine like terms: -8.024376923 + -2.765 = -10.789376923 x = -10.789376923 Simplifying x = -10.789376923Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.259376923, -10.789376923}
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