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Simplifying x2 + -2x + 14x = 54 Reorder the terms: -2x + 14x + x2 = 54 Combine like terms: -2x + 14x = 12x 12x + x2 = 54 Solving 12x + x2 = 54 Solving for variable 'x'. Reorder the terms: -54 + 12x + x2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + 12x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + 12x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 12x + x2 = 0 + 54 12x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 12x + x2 = 54 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 54 + 36 Reorder the terms: 36 + 12x + x2 = 54 + 36 Combine like terms: 54 + 36 = 90 36 + 12x + x2 = 90 Factor a perfect square on the left side: (x + 6)(x + 6) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (x + 6) equal to 9.486832981 and -9.486832981.Subproblem 1
x + 6 = 9.486832981 Simplifying x + 6 = 9.486832981 Reorder the terms: 6 + x = 9.486832981 Solving 6 + x = 9.486832981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 9.486832981 + -6 Combine like terms: 6 + -6 = 0 0 + x = 9.486832981 + -6 x = 9.486832981 + -6 Combine like terms: 9.486832981 + -6 = 3.486832981 x = 3.486832981 Simplifying x = 3.486832981Subproblem 2
x + 6 = -9.486832981 Simplifying x + 6 = -9.486832981 Reorder the terms: 6 + x = -9.486832981 Solving 6 + x = -9.486832981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -9.486832981 + -6 Combine like terms: 6 + -6 = 0 0 + x = -9.486832981 + -6 x = -9.486832981 + -6 Combine like terms: -9.486832981 + -6 = -15.486832981 x = -15.486832981 Simplifying x = -15.486832981Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.486832981, -15.486832981}
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