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Simplifying 48 = x(x + 12) Reorder the terms: 48 = x(12 + x) 48 = (12 * x + x * x) 48 = (12x + x2) Solving 48 = 12x + x2 Solving for variable 'x'. Reorder the terms: 48 + -12x + -1x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 48 + -12x + -1x2 = 0 + x2 + -1x2 48 + -12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 48 + -12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -48 + 12x + x2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + 12x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + 12x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 12x + x2 = 0 + 48 12x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 12x + x2 = 48 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 = 48 + 36 Reorder the terms: 36 + 12x + x2 = 48 + 36 Combine like terms: 48 + 36 = 84 36 + 12x + x2 = 84 Factor a perfect square on the left side: (x + 6)(x + 6) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (x + 6) equal to 9.16515139 and -9.16515139.Subproblem 1
x + 6 = 9.16515139 Simplifying x + 6 = 9.16515139 Reorder the terms: 6 + x = 9.16515139 Solving 6 + x = 9.16515139 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 = 9.16515139 + -6 Combine like terms: 6 + -6 = 0 0 + x = 9.16515139 + -6 x = 9.16515139 + -6 Combine like terms: 9.16515139 + -6 = 3.16515139 x = 3.16515139 Simplifying x = 3.16515139Subproblem 2
x + 6 = -9.16515139 Simplifying x + 6 = -9.16515139 Reorder the terms: 6 + x = -9.16515139 Solving 6 + x = -9.16515139 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 = -9.16515139 + -6 Combine like terms: 6 + -6 = 0 0 + x = -9.16515139 + -6 x = -9.16515139 + -6 Combine like terms: -9.16515139 + -6 = -15.16515139 x = -15.16515139 Simplifying x = -15.16515139Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.16515139, -15.16515139}
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