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Simplifying 25x2 + 10x + 1 + x2 + 2x + 4 = 25x2 Reorder the terms: 1 + 4 + 10x + 2x + 25x2 + x2 = 25x2 Combine like terms: 1 + 4 = 5 5 + 10x + 2x + 25x2 + x2 = 25x2 Combine like terms: 10x + 2x = 12x 5 + 12x + 25x2 + x2 = 25x2 Combine like terms: 25x2 + x2 = 26x2 5 + 12x + 26x2 = 25x2 Solving 5 + 12x + 26x2 = 25x2 Solving for variable 'x'. Combine like terms: 26x2 + -25x2 = 1x2 5 + 12x + 1x2 = 25x2 + -25x2 Combine like terms: 25x2 + -25x2 = 0 5 + 12x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 12x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 12x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 12x + x2 = 0 + -5 12x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 12x + x2 = -5 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = -5 + 36 Reorder the terms: 36 + 12x + x2 = -5 + 36 Combine like terms: -5 + 36 = 31 36 + 12x + x2 = 31 Factor a perfect square on the left side: (x + 6)(x + 6) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (x + 6) equal to 5.567764363 and -5.567764363.Subproblem 1
x + 6 = 5.567764363 Simplifying x + 6 = 5.567764363 Reorder the terms: 6 + x = 5.567764363 Solving 6 + x = 5.567764363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 5.567764363 + -6 Combine like terms: 6 + -6 = 0 0 + x = 5.567764363 + -6 x = 5.567764363 + -6 Combine like terms: 5.567764363 + -6 = -0.432235637 x = -0.432235637 Simplifying x = -0.432235637Subproblem 2
x + 6 = -5.567764363 Simplifying x + 6 = -5.567764363 Reorder the terms: 6 + x = -5.567764363 Solving 6 + x = -5.567764363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -5.567764363 + -6 Combine like terms: 6 + -6 = 0 0 + x = -5.567764363 + -6 x = -5.567764363 + -6 Combine like terms: -5.567764363 + -6 = -11.567764363 x = -11.567764363 Simplifying x = -11.567764363Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.432235637, -11.567764363}
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