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Simplifying 3x + 2x(x + 2) = 14 Reorder the terms: 3x + 2x(2 + x) = 14 3x + (2 * 2x + x * 2x) = 14 3x + (4x + 2x2) = 14 Combine like terms: 3x + 4x = 7x 7x + 2x2 = 14 Solving 7x + 2x2 = 14 Solving for variable 'x'. Reorder the terms: -14 + 7x + 2x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7 + 3.5x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 3.5x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 3.5x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 3.5x + x2 = 0 + 7 3.5x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 3.5x + x2 = 7 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 7 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 7 + 3.0625 Combine like terms: 7 + 3.0625 = 10.0625 3.0625 + 3.5x + x2 = 10.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 10.0625 Calculate the square root of the right side: 3.172144385 Break this problem into two subproblems by setting (x + 1.75) equal to 3.172144385 and -3.172144385.Subproblem 1
x + 1.75 = 3.172144385 Simplifying x + 1.75 = 3.172144385 Reorder the terms: 1.75 + x = 3.172144385 Solving 1.75 + x = 3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 3.172144385 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 3.172144385 + -1.75 x = 3.172144385 + -1.75 Combine like terms: 3.172144385 + -1.75 = 1.422144385 x = 1.422144385 Simplifying x = 1.422144385Subproblem 2
x + 1.75 = -3.172144385 Simplifying x + 1.75 = -3.172144385 Reorder the terms: 1.75 + x = -3.172144385 Solving 1.75 + x = -3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -3.172144385 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -3.172144385 + -1.75 x = -3.172144385 + -1.75 Combine like terms: -3.172144385 + -1.75 = -4.922144385 x = -4.922144385 Simplifying x = -4.922144385Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.422144385, -4.922144385}
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