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Simplifying (5x + -2)(5x + 2) = 25x + -7x Reorder the terms: (-2 + 5x)(5x + 2) = 25x + -7x Reorder the terms: (-2 + 5x)(2 + 5x) = 25x + -7x Multiply (-2 + 5x) * (2 + 5x) (-2(2 + 5x) + 5x * (2 + 5x)) = 25x + -7x ((2 * -2 + 5x * -2) + 5x * (2 + 5x)) = 25x + -7x ((-4 + -10x) + 5x * (2 + 5x)) = 25x + -7x (-4 + -10x + (2 * 5x + 5x * 5x)) = 25x + -7x (-4 + -10x + (10x + 25x2)) = 25x + -7x Combine like terms: -10x + 10x = 0 (-4 + 0 + 25x2) = 25x + -7x (-4 + 25x2) = 25x + -7x Combine like terms: 25x + -7x = 18x -4 + 25x2 = 18x Solving -4 + 25x2 = 18x Solving for variable 'x'. Reorder the terms: -4 + -18x + 25x2 = 18x + -18x Combine like terms: 18x + -18x = 0 -4 + -18x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.16 + -0.72x + x2 = 0 Move the constant term to the right: Add '0.16' to each side of the equation. -0.16 + -0.72x + 0.16 + x2 = 0 + 0.16 Reorder the terms: -0.16 + 0.16 + -0.72x + x2 = 0 + 0.16 Combine like terms: -0.16 + 0.16 = 0.00 0.00 + -0.72x + x2 = 0 + 0.16 -0.72x + x2 = 0 + 0.16 Combine like terms: 0 + 0.16 = 0.16 -0.72x + x2 = 0.16 The x term is -0.72x. Take half its coefficient (-0.36). Square it (0.1296) and add it to both sides. Add '0.1296' to each side of the equation. -0.72x + 0.1296 + x2 = 0.16 + 0.1296 Reorder the terms: 0.1296 + -0.72x + x2 = 0.16 + 0.1296 Combine like terms: 0.16 + 0.1296 = 0.2896 0.1296 + -0.72x + x2 = 0.2896 Factor a perfect square on the left side: (x + -0.36)(x + -0.36) = 0.2896 Calculate the square root of the right side: 0.538144962 Break this problem into two subproblems by setting (x + -0.36) equal to 0.538144962 and -0.538144962.Subproblem 1
x + -0.36 = 0.538144962 Simplifying x + -0.36 = 0.538144962 Reorder the terms: -0.36 + x = 0.538144962 Solving -0.36 + x = 0.538144962 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.36' to each side of the equation. -0.36 + 0.36 + x = 0.538144962 + 0.36 Combine like terms: -0.36 + 0.36 = 0.00 0.00 + x = 0.538144962 + 0.36 x = 0.538144962 + 0.36 Combine like terms: 0.538144962 + 0.36 = 0.898144962 x = 0.898144962 Simplifying x = 0.898144962Subproblem 2
x + -0.36 = -0.538144962 Simplifying x + -0.36 = -0.538144962 Reorder the terms: -0.36 + x = -0.538144962 Solving -0.36 + x = -0.538144962 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.36' to each side of the equation. -0.36 + 0.36 + x = -0.538144962 + 0.36 Combine like terms: -0.36 + 0.36 = 0.00 0.00 + x = -0.538144962 + 0.36 x = -0.538144962 + 0.36 Combine like terms: -0.538144962 + 0.36 = -0.178144962 x = -0.178144962 Simplifying x = -0.178144962Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.898144962, -0.178144962}
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