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Simplifying x2 + 12x = 780 Reorder the terms: 12x + x2 = 780 Solving 12x + x2 = 780 Solving for variable 'x'. Reorder the terms: -780 + 12x + x2 = 780 + -780 Combine like terms: 780 + -780 = 0 -780 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '780' to each side of the equation. -780 + 12x + 780 + x2 = 0 + 780 Reorder the terms: -780 + 780 + 12x + x2 = 0 + 780 Combine like terms: -780 + 780 = 0 0 + 12x + x2 = 0 + 780 12x + x2 = 0 + 780 Combine like terms: 0 + 780 = 780 12x + x2 = 780 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 = 780 + 36 Reorder the terms: 36 + 12x + x2 = 780 + 36 Combine like terms: 780 + 36 = 816 36 + 12x + x2 = 816 Factor a perfect square on the left side: (x + 6)(x + 6) = 816 Calculate the square root of the right side: 28.565713714 Break this problem into two subproblems by setting (x + 6) equal to 28.565713714 and -28.565713714.Subproblem 1
x + 6 = 28.565713714 Simplifying x + 6 = 28.565713714 Reorder the terms: 6 + x = 28.565713714 Solving 6 + x = 28.565713714 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 = 28.565713714 + -6 Combine like terms: 6 + -6 = 0 0 + x = 28.565713714 + -6 x = 28.565713714 + -6 Combine like terms: 28.565713714 + -6 = 22.565713714 x = 22.565713714 Simplifying x = 22.565713714Subproblem 2
x + 6 = -28.565713714 Simplifying x + 6 = -28.565713714 Reorder the terms: 6 + x = -28.565713714 Solving 6 + x = -28.565713714 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 = -28.565713714 + -6 Combine like terms: 6 + -6 = 0 0 + x = -28.565713714 + -6 x = -28.565713714 + -6 Combine like terms: -28.565713714 + -6 = -34.565713714 x = -34.565713714 Simplifying x = -34.565713714Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.565713714, -34.565713714}
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