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Simplifying 0 = 3x2 + 36x + -100 Reorder the terms: 0 = -100 + 36x + 3x2 Solving 0 = -100 + 36x + 3x2 Solving for variable 'x'. Combine like terms: 0 + 100 = 100 100 + -36x + -3x2 = -100 + 36x + 3x2 + 100 + -36x + -3x2 Reorder the terms: 100 + -36x + -3x2 = -100 + 100 + 36x + -36x + 3x2 + -3x2 Combine like terms: -100 + 100 = 0 100 + -36x + -3x2 = 0 + 36x + -36x + 3x2 + -3x2 100 + -36x + -3x2 = 36x + -36x + 3x2 + -3x2 Combine like terms: 36x + -36x = 0 100 + -36x + -3x2 = 0 + 3x2 + -3x2 100 + -36x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 100 + -36x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -33.33333333 + 12x + x2 = 0 Move the constant term to the right: Add '33.33333333' to each side of the equation. -33.33333333 + 12x + 33.33333333 + x2 = 0 + 33.33333333 Reorder the terms: -33.33333333 + 33.33333333 + 12x + x2 = 0 + 33.33333333 Combine like terms: -33.33333333 + 33.33333333 = 0.00000000 0.00000000 + 12x + x2 = 0 + 33.33333333 12x + x2 = 0 + 33.33333333 Combine like terms: 0 + 33.33333333 = 33.33333333 12x + x2 = 33.33333333 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 = 33.33333333 + 36 Reorder the terms: 36 + 12x + x2 = 33.33333333 + 36 Combine like terms: 33.33333333 + 36 = 69.33333333 36 + 12x + x2 = 69.33333333 Factor a perfect square on the left side: (x + 6)(x + 6) = 69.33333333 Calculate the square root of the right side: 8.326663998 Break this problem into two subproblems by setting (x + 6) equal to 8.326663998 and -8.326663998.Subproblem 1
x + 6 = 8.326663998 Simplifying x + 6 = 8.326663998 Reorder the terms: 6 + x = 8.326663998 Solving 6 + x = 8.326663998 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 = 8.326663998 + -6 Combine like terms: 6 + -6 = 0 0 + x = 8.326663998 + -6 x = 8.326663998 + -6 Combine like terms: 8.326663998 + -6 = 2.326663998 x = 2.326663998 Simplifying x = 2.326663998Subproblem 2
x + 6 = -8.326663998 Simplifying x + 6 = -8.326663998 Reorder the terms: 6 + x = -8.326663998 Solving 6 + x = -8.326663998 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 = -8.326663998 + -6 Combine like terms: 6 + -6 = 0 0 + x = -8.326663998 + -6 x = -8.326663998 + -6 Combine like terms: -8.326663998 + -6 = -14.326663998 x = -14.326663998 Simplifying x = -14.326663998Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.326663998, -14.326663998}
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