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Simplifying 144 = x(x + 6) Reorder the terms: 144 = x(6 + x) 144 = (6 * x + x * x) 144 = (6x + x2) Solving 144 = 6x + x2 Solving for variable 'x'. Reorder the terms: 144 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 144 + -6x + -1x2 = 0 + x2 + -1x2 144 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 144 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -144 + 6x + x2 = 0 Move the constant term to the right: Add '144' to each side of the equation. -144 + 6x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + 6x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 6x + x2 = 0 + 144 6x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 6x + x2 = 144 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 144 + 9 Reorder the terms: 9 + 6x + x2 = 144 + 9 Combine like terms: 144 + 9 = 153 9 + 6x + x2 = 153 Factor a perfect square on the left side: (x + 3)(x + 3) = 153 Calculate the square root of the right side: 12.369316877 Break this problem into two subproblems by setting (x + 3) equal to 12.369316877 and -12.369316877.Subproblem 1
x + 3 = 12.369316877 Simplifying x + 3 = 12.369316877 Reorder the terms: 3 + x = 12.369316877 Solving 3 + x = 12.369316877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 12.369316877 + -3 Combine like terms: 3 + -3 = 0 0 + x = 12.369316877 + -3 x = 12.369316877 + -3 Combine like terms: 12.369316877 + -3 = 9.369316877 x = 9.369316877 Simplifying x = 9.369316877Subproblem 2
x + 3 = -12.369316877 Simplifying x + 3 = -12.369316877 Reorder the terms: 3 + x = -12.369316877 Solving 3 + x = -12.369316877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -12.369316877 + -3 Combine like terms: 3 + -3 = 0 0 + x = -12.369316877 + -3 x = -12.369316877 + -3 Combine like terms: -12.369316877 + -3 = -15.369316877 x = -15.369316877 Simplifying x = -15.369316877Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.369316877, -15.369316877}
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