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Simplifying 49 = 12x + x2 Solving 49 = 12x + x2 Solving for variable 'x'. Reorder the terms: 49 + -12x + -1x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 49 + -12x + -1x2 = 0 + x2 + -1x2 49 + -12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 49 + -12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -49 + 12x + x2 = 0 Move the constant term to the right: Add '49' to each side of the equation. -49 + 12x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + 12x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 12x + x2 = 0 + 49 12x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 12x + x2 = 49 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 = 49 + 36 Reorder the terms: 36 + 12x + x2 = 49 + 36 Combine like terms: 49 + 36 = 85 36 + 12x + x2 = 85 Factor a perfect square on the left side: (x + 6)(x + 6) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (x + 6) equal to 9.219544457 and -9.219544457.Subproblem 1
x + 6 = 9.219544457 Simplifying x + 6 = 9.219544457 Reorder the terms: 6 + x = 9.219544457 Solving 6 + x = 9.219544457 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 = 9.219544457 + -6 Combine like terms: 6 + -6 = 0 0 + x = 9.219544457 + -6 x = 9.219544457 + -6 Combine like terms: 9.219544457 + -6 = 3.219544457 x = 3.219544457 Simplifying x = 3.219544457Subproblem 2
x + 6 = -9.219544457 Simplifying x + 6 = -9.219544457 Reorder the terms: 6 + x = -9.219544457 Solving 6 + x = -9.219544457 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 = -9.219544457 + -6 Combine like terms: 6 + -6 = 0 0 + x = -9.219544457 + -6 x = -9.219544457 + -6 Combine like terms: -9.219544457 + -6 = -15.219544457 x = -15.219544457 Simplifying x = -15.219544457Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.219544457, -15.219544457}
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