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Simplifying 2x(x + 3) = 47 Reorder the terms: 2x(3 + x) = 47 (3 * 2x + x * 2x) = 47 (6x + 2x2) = 47 Solving 6x + 2x2 = 47 Solving for variable 'x'. Reorder the terms: -47 + 6x + 2x2 = 47 + -47 Combine like terms: 47 + -47 = 0 -47 + 6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -23.5 + 3x + x2 = 0 Move the constant term to the right: Add '23.5' to each side of the equation. -23.5 + 3x + 23.5 + x2 = 0 + 23.5 Reorder the terms: -23.5 + 23.5 + 3x + x2 = 0 + 23.5 Combine like terms: -23.5 + 23.5 = 0.0 0.0 + 3x + x2 = 0 + 23.5 3x + x2 = 0 + 23.5 Combine like terms: 0 + 23.5 = 23.5 3x + x2 = 23.5 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 23.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 23.5 + 2.25 Combine like terms: 23.5 + 2.25 = 25.75 2.25 + 3x + x2 = 25.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 25.75 Calculate the square root of the right side: 5.074445783 Break this problem into two subproblems by setting (x + 1.5) equal to 5.074445783 and -5.074445783.Subproblem 1
x + 1.5 = 5.074445783 Simplifying x + 1.5 = 5.074445783 Reorder the terms: 1.5 + x = 5.074445783 Solving 1.5 + x = 5.074445783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 5.074445783 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 5.074445783 + -1.5 x = 5.074445783 + -1.5 Combine like terms: 5.074445783 + -1.5 = 3.574445783 x = 3.574445783 Simplifying x = 3.574445783Subproblem 2
x + 1.5 = -5.074445783 Simplifying x + 1.5 = -5.074445783 Reorder the terms: 1.5 + x = -5.074445783 Solving 1.5 + x = -5.074445783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -5.074445783 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -5.074445783 + -1.5 x = -5.074445783 + -1.5 Combine like terms: -5.074445783 + -1.5 = -6.574445783 x = -6.574445783 Simplifying x = -6.574445783Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.574445783, -6.574445783}
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