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Simplifying x2 + (2x) * 2 = 625 Remove parenthesis around (2x) x2 + 2x * 2 = 625 Reorder the terms for easier multiplication: x2 + 2 * 2x = 625 Multiply 2 * 2 x2 + 4x = 625 Reorder the terms: 4x + x2 = 625 Solving 4x + x2 = 625 Solving for variable 'x'. Reorder the terms: -625 + 4x + x2 = 625 + -625 Combine like terms: 625 + -625 = 0 -625 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '625' to each side of the equation. -625 + 4x + 625 + x2 = 0 + 625 Reorder the terms: -625 + 625 + 4x + x2 = 0 + 625 Combine like terms: -625 + 625 = 0 0 + 4x + x2 = 0 + 625 4x + x2 = 0 + 625 Combine like terms: 0 + 625 = 625 4x + x2 = 625 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 625 + 4 Reorder the terms: 4 + 4x + x2 = 625 + 4 Combine like terms: 625 + 4 = 629 4 + 4x + x2 = 629 Factor a perfect square on the left side: (x + 2)(x + 2) = 629 Calculate the square root of the right side: 25.079872408 Break this problem into two subproblems by setting (x + 2) equal to 25.079872408 and -25.079872408.Subproblem 1
x + 2 = 25.079872408 Simplifying x + 2 = 25.079872408 Reorder the terms: 2 + x = 25.079872408 Solving 2 + x = 25.079872408 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 25.079872408 + -2 Combine like terms: 2 + -2 = 0 0 + x = 25.079872408 + -2 x = 25.079872408 + -2 Combine like terms: 25.079872408 + -2 = 23.079872408 x = 23.079872408 Simplifying x = 23.079872408Subproblem 2
x + 2 = -25.079872408 Simplifying x + 2 = -25.079872408 Reorder the terms: 2 + x = -25.079872408 Solving 2 + x = -25.079872408 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -25.079872408 + -2 Combine like terms: 2 + -2 = 0 0 + x = -25.079872408 + -2 x = -25.079872408 + -2 Combine like terms: -25.079872408 + -2 = -27.079872408 x = -27.079872408 Simplifying x = -27.079872408Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.079872408, -27.079872408}
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