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Simplifying (4x + 2)(x + 5) = 5x(x + -5) Reorder the terms: (2 + 4x)(x + 5) = 5x(x + -5) Reorder the terms: (2 + 4x)(5 + x) = 5x(x + -5) Multiply (2 + 4x) * (5 + x) (2(5 + x) + 4x * (5 + x)) = 5x(x + -5) ((5 * 2 + x * 2) + 4x * (5 + x)) = 5x(x + -5) ((10 + 2x) + 4x * (5 + x)) = 5x(x + -5) (10 + 2x + (5 * 4x + x * 4x)) = 5x(x + -5) (10 + 2x + (20x + 4x2)) = 5x(x + -5) Combine like terms: 2x + 20x = 22x (10 + 22x + 4x2) = 5x(x + -5) Reorder the terms: 10 + 22x + 4x2 = 5x(-5 + x) 10 + 22x + 4x2 = (-5 * 5x + x * 5x) 10 + 22x + 4x2 = (-25x + 5x2) Solving 10 + 22x + 4x2 = -25x + 5x2 Solving for variable 'x'. Reorder the terms: 10 + 22x + 25x + 4x2 + -5x2 = -25x + 5x2 + 25x + -5x2 Combine like terms: 22x + 25x = 47x 10 + 47x + 4x2 + -5x2 = -25x + 5x2 + 25x + -5x2 Combine like terms: 4x2 + -5x2 = -1x2 10 + 47x + -1x2 = -25x + 5x2 + 25x + -5x2 Reorder the terms: 10 + 47x + -1x2 = -25x + 25x + 5x2 + -5x2 Combine like terms: -25x + 25x = 0 10 + 47x + -1x2 = 0 + 5x2 + -5x2 10 + 47x + -1x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 10 + 47x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10 + -47x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -47x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -47x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -47x + x2 = 0 + 10 -47x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -47x + x2 = 10 The x term is -47x. Take half its coefficient (-23.5). Square it (552.25) and add it to both sides. Add '552.25' to each side of the equation. -47x + 552.25 + x2 = 10 + 552.25 Reorder the terms: 552.25 + -47x + x2 = 10 + 552.25 Combine like terms: 10 + 552.25 = 562.25 552.25 + -47x + x2 = 562.25 Factor a perfect square on the left side: (x + -23.5)(x + -23.5) = 562.25 Calculate the square root of the right side: 23.711811403 Break this problem into two subproblems by setting (x + -23.5) equal to 23.711811403 and -23.711811403.Subproblem 1
x + -23.5 = 23.711811403 Simplifying x + -23.5 = 23.711811403 Reorder the terms: -23.5 + x = 23.711811403 Solving -23.5 + x = 23.711811403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23.5' to each side of the equation. -23.5 + 23.5 + x = 23.711811403 + 23.5 Combine like terms: -23.5 + 23.5 = 0.0 0.0 + x = 23.711811403 + 23.5 x = 23.711811403 + 23.5 Combine like terms: 23.711811403 + 23.5 = 47.211811403 x = 47.211811403 Simplifying x = 47.211811403Subproblem 2
x + -23.5 = -23.711811403 Simplifying x + -23.5 = -23.711811403 Reorder the terms: -23.5 + x = -23.711811403 Solving -23.5 + x = -23.711811403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23.5' to each side of the equation. -23.5 + 23.5 + x = -23.711811403 + 23.5 Combine like terms: -23.5 + 23.5 = 0.0 0.0 + x = -23.711811403 + 23.5 x = -23.711811403 + 23.5 Combine like terms: -23.711811403 + 23.5 = -0.211811403 x = -0.211811403 Simplifying x = -0.211811403Solution
The solution to the problem is based on the solutions from the subproblems. x = {47.211811403, -0.211811403}
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