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Simplifying (5x + -2)(5x + -2) = 184 Reorder the terms: (-2 + 5x)(5x + -2) = 184 Reorder the terms: (-2 + 5x)(-2 + 5x) = 184 Multiply (-2 + 5x) * (-2 + 5x) (-2(-2 + 5x) + 5x * (-2 + 5x)) = 184 ((-2 * -2 + 5x * -2) + 5x * (-2 + 5x)) = 184 ((4 + -10x) + 5x * (-2 + 5x)) = 184 (4 + -10x + (-2 * 5x + 5x * 5x)) = 184 (4 + -10x + (-10x + 25x2)) = 184 Combine like terms: -10x + -10x = -20x (4 + -20x + 25x2) = 184 Solving 4 + -20x + 25x2 = 184 Solving for variable 'x'. Reorder the terms: 4 + -184 + -20x + 25x2 = 184 + -184 Combine like terms: 4 + -184 = -180 -180 + -20x + 25x2 = 184 + -184 Combine like terms: 184 + -184 = 0 -180 + -20x + 25x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-36 + -4x + 5x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-36 + -4x + 5x2)' equal to zero and attempt to solve: Simplifying -36 + -4x + 5x2 = 0 Solving -36 + -4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7.2 + -0.8x + x2 = 0 Move the constant term to the right: Add '7.2' to each side of the equation. -7.2 + -0.8x + 7.2 + x2 = 0 + 7.2 Reorder the terms: -7.2 + 7.2 + -0.8x + x2 = 0 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + -0.8x + x2 = 0 + 7.2 -0.8x + x2 = 0 + 7.2 Combine like terms: 0 + 7.2 = 7.2 -0.8x + x2 = 7.2 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 7.2 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 7.2 + 0.16 Combine like terms: 7.2 + 0.16 = 7.36 0.16 + -0.8x + x2 = 7.36 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 7.36 Calculate the square root of the right side: 2.712931993 Break this problem into two subproblems by setting (x + -0.4) equal to 2.712931993 and -2.712931993.Subproblem 1
x + -0.4 = 2.712931993 Simplifying x + -0.4 = 2.712931993 Reorder the terms: -0.4 + x = 2.712931993 Solving -0.4 + x = 2.712931993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 2.712931993 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 2.712931993 + 0.4 x = 2.712931993 + 0.4 Combine like terms: 2.712931993 + 0.4 = 3.112931993 x = 3.112931993 Simplifying x = 3.112931993Subproblem 2
x + -0.4 = -2.712931993 Simplifying x + -0.4 = -2.712931993 Reorder the terms: -0.4 + x = -2.712931993 Solving -0.4 + x = -2.712931993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -2.712931993 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -2.712931993 + 0.4 x = -2.712931993 + 0.4 Combine like terms: -2.712931993 + 0.4 = -2.312931993 x = -2.312931993 Simplifying x = -2.312931993Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.112931993, -2.312931993}Solution
x = {3.112931993, -2.312931993}
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