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Simplifying (7.3x)(x + 2) = 4 Remove parenthesis around (7.3x) 7.3x(x + 2) = 4 Reorder the terms: 7.3x(2 + x) = 4 (2 * 7.3x + x * 7.3x) = 4 (14.6x + 7.3x2) = 4 Solving 14.6x + 7.3x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + 14.6x + 7.3x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 14.6x + 7.3x2 = 0 Begin completing the square. Divide all terms by 7.3 the coefficient of the squared term: Divide each side by '7.3'. -0.5479452055 + 2x + x2 = 0 Move the constant term to the right: Add '0.5479452055' to each side of the equation. -0.5479452055 + 2x + 0.5479452055 + x2 = 0 + 0.5479452055 Reorder the terms: -0.5479452055 + 0.5479452055 + 2x + x2 = 0 + 0.5479452055 Combine like terms: -0.5479452055 + 0.5479452055 = 0.0000000000 0.0000000000 + 2x + x2 = 0 + 0.5479452055 2x + x2 = 0 + 0.5479452055 Combine like terms: 0 + 0.5479452055 = 0.5479452055 2x + x2 = 0.5479452055 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 = 0.5479452055 + 1 Reorder the terms: 1 + 2x + x2 = 0.5479452055 + 1 Combine like terms: 0.5479452055 + 1 = 1.5479452055 1 + 2x + x2 = 1.5479452055 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.5479452055 Calculate the square root of the right side: 1.244164461 Break this problem into two subproblems by setting (x + 1) equal to 1.244164461 and -1.244164461.Subproblem 1
x + 1 = 1.244164461 Simplifying x + 1 = 1.244164461 Reorder the terms: 1 + x = 1.244164461 Solving 1 + x = 1.244164461 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 = 1.244164461 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.244164461 + -1 x = 1.244164461 + -1 Combine like terms: 1.244164461 + -1 = 0.244164461 x = 0.244164461 Simplifying x = 0.244164461Subproblem 2
x + 1 = -1.244164461 Simplifying x + 1 = -1.244164461 Reorder the terms: 1 + x = -1.244164461 Solving 1 + x = -1.244164461 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 = -1.244164461 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.244164461 + -1 x = -1.244164461 + -1 Combine like terms: -1.244164461 + -1 = -2.244164461 x = -2.244164461 Simplifying x = -2.244164461Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.244164461, -2.244164461}
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