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Simplifying x2 = 8x + 74 Reorder the terms: x2 = 74 + 8x Solving x2 = 74 + 8x Solving for variable 'x'. Reorder the terms: -74 + -8x + x2 = 74 + 8x + -74 + -8x Reorder the terms: -74 + -8x + x2 = 74 + -74 + 8x + -8x Combine like terms: 74 + -74 = 0 -74 + -8x + x2 = 0 + 8x + -8x -74 + -8x + x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -74 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '74' to each side of the equation. -74 + -8x + 74 + x2 = 0 + 74 Reorder the terms: -74 + 74 + -8x + x2 = 0 + 74 Combine like terms: -74 + 74 = 0 0 + -8x + x2 = 0 + 74 -8x + x2 = 0 + 74 Combine like terms: 0 + 74 = 74 -8x + x2 = 74 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 74 + 16 Reorder the terms: 16 + -8x + x2 = 74 + 16 Combine like terms: 74 + 16 = 90 16 + -8x + x2 = 90 Factor a perfect square on the left side: (x + -4)(x + -4) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (x + -4) equal to 9.486832981 and -9.486832981.Subproblem 1
x + -4 = 9.486832981 Simplifying x + -4 = 9.486832981 Reorder the terms: -4 + x = 9.486832981 Solving -4 + x = 9.486832981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 9.486832981 + 4 Combine like terms: -4 + 4 = 0 0 + x = 9.486832981 + 4 x = 9.486832981 + 4 Combine like terms: 9.486832981 + 4 = 13.486832981 x = 13.486832981 Simplifying x = 13.486832981Subproblem 2
x + -4 = -9.486832981 Simplifying x + -4 = -9.486832981 Reorder the terms: -4 + x = -9.486832981 Solving -4 + x = -9.486832981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -9.486832981 + 4 Combine like terms: -4 + 4 = 0 0 + x = -9.486832981 + 4 x = -9.486832981 + 4 Combine like terms: -9.486832981 + 4 = -5.486832981 x = -5.486832981 Simplifying x = -5.486832981Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.486832981, -5.486832981}
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