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Simplifying 2x2 = x + 2(x + 2 + 2x + 5) Reorder the terms: 2x2 = x + 2(2 + 5 + x + 2x) Combine like terms: 2 + 5 = 7 2x2 = x + 2(7 + x + 2x) Combine like terms: x + 2x = 3x 2x2 = x + 2(7 + 3x) 2x2 = x + (7 * 2 + 3x * 2) 2x2 = x + (14 + 6x) Reorder the terms: 2x2 = 14 + x + 6x Combine like terms: x + 6x = 7x 2x2 = 14 + 7x Solving 2x2 = 14 + 7x Solving for variable 'x'. Reorder the terms: -14 + -7x + 2x2 = 14 + 7x + -14 + -7x Reorder the terms: -14 + -7x + 2x2 = 14 + -14 + 7x + -7x Combine like terms: 14 + -14 = 0 -14 + -7x + 2x2 = 0 + 7x + -7x -14 + -7x + 2x2 = 7x + -7x Combine like terms: 7x + -7x = 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 = 4.922144385 x = 4.922144385 Simplifying x = 4.922144385Subproblem 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 = -1.422144385 x = -1.422144385 Simplifying x = -1.422144385Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.922144385, -1.422144385}
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