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Simplifying 2x2 + 12x + 36 = 91 Reorder the terms: 36 + 12x + 2x2 = 91 Solving 36 + 12x + 2x2 = 91 Solving for variable 'x'. Reorder the terms: 36 + -91 + 12x + 2x2 = 91 + -91 Combine like terms: 36 + -91 = -55 -55 + 12x + 2x2 = 91 + -91 Combine like terms: 91 + -91 = 0 -55 + 12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -27.5 + 6x + x2 = 0 Move the constant term to the right: Add '27.5' to each side of the equation. -27.5 + 6x + 27.5 + x2 = 0 + 27.5 Reorder the terms: -27.5 + 27.5 + 6x + x2 = 0 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + 6x + x2 = 0 + 27.5 6x + x2 = 0 + 27.5 Combine like terms: 0 + 27.5 = 27.5 6x + x2 = 27.5 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 = 27.5 + 9 Reorder the terms: 9 + 6x + x2 = 27.5 + 9 Combine like terms: 27.5 + 9 = 36.5 9 + 6x + x2 = 36.5 Factor a perfect square on the left side: (x + 3)(x + 3) = 36.5 Calculate the square root of the right side: 6.041522987 Break this problem into two subproblems by setting (x + 3) equal to 6.041522987 and -6.041522987.Subproblem 1
x + 3 = 6.041522987 Simplifying x + 3 = 6.041522987 Reorder the terms: 3 + x = 6.041522987 Solving 3 + x = 6.041522987 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 = 6.041522987 + -3 Combine like terms: 3 + -3 = 0 0 + x = 6.041522987 + -3 x = 6.041522987 + -3 Combine like terms: 6.041522987 + -3 = 3.041522987 x = 3.041522987 Simplifying x = 3.041522987Subproblem 2
x + 3 = -6.041522987 Simplifying x + 3 = -6.041522987 Reorder the terms: 3 + x = -6.041522987 Solving 3 + x = -6.041522987 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 = -6.041522987 + -3 Combine like terms: 3 + -3 = 0 0 + x = -6.041522987 + -3 x = -6.041522987 + -3 Combine like terms: -6.041522987 + -3 = -9.041522987 x = -9.041522987 Simplifying x = -9.041522987Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.041522987, -9.041522987}
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