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Simplifying x2 + 30x + 1 = 8(5x + -2) Reorder the terms: 1 + 30x + x2 = 8(5x + -2) Reorder the terms: 1 + 30x + x2 = 8(-2 + 5x) 1 + 30x + x2 = (-2 * 8 + 5x * 8) 1 + 30x + x2 = (-16 + 40x) Solving 1 + 30x + x2 = -16 + 40x Solving for variable 'x'. Reorder the terms: 1 + 16 + 30x + -40x + x2 = -16 + 40x + 16 + -40x Combine like terms: 1 + 16 = 17 17 + 30x + -40x + x2 = -16 + 40x + 16 + -40x Combine like terms: 30x + -40x = -10x 17 + -10x + x2 = -16 + 40x + 16 + -40x Reorder the terms: 17 + -10x + x2 = -16 + 16 + 40x + -40x Combine like terms: -16 + 16 = 0 17 + -10x + x2 = 0 + 40x + -40x 17 + -10x + x2 = 40x + -40x Combine like terms: 40x + -40x = 0 17 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + -10x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + -10x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -10x + x2 = 0 + -17 -10x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 -10x + x2 = -17 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -17 + 25 Reorder the terms: 25 + -10x + x2 = -17 + 25 Combine like terms: -17 + 25 = 8 25 + -10x + x2 = 8 Factor a perfect square on the left side: (x + -5)(x + -5) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + -5) equal to 2.828427125 and -2.828427125.Subproblem 1
x + -5 = 2.828427125 Simplifying x + -5 = 2.828427125 Reorder the terms: -5 + x = 2.828427125 Solving -5 + x = 2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 2.828427125 + 5 Combine like terms: -5 + 5 = 0 0 + x = 2.828427125 + 5 x = 2.828427125 + 5 Combine like terms: 2.828427125 + 5 = 7.828427125 x = 7.828427125 Simplifying x = 7.828427125Subproblem 2
x + -5 = -2.828427125 Simplifying x + -5 = -2.828427125 Reorder the terms: -5 + x = -2.828427125 Solving -5 + x = -2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -2.828427125 + 5 Combine like terms: -5 + 5 = 0 0 + x = -2.828427125 + 5 x = -2.828427125 + 5 Combine like terms: -2.828427125 + 5 = 2.171572875 x = 2.171572875 Simplifying x = 2.171572875Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.828427125, 2.171572875}
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