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Simplifying 3x2 + 18x + -56 = 0 Reorder the terms: -56 + 18x + 3x2 = 0 Solving -56 + 18x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -18.66666667 + 6x + x2 = 0 Move the constant term to the right: Add '18.66666667' to each side of the equation. -18.66666667 + 6x + 18.66666667 + x2 = 0 + 18.66666667 Reorder the terms: -18.66666667 + 18.66666667 + 6x + x2 = 0 + 18.66666667 Combine like terms: -18.66666667 + 18.66666667 = 0.00000000 0.00000000 + 6x + x2 = 0 + 18.66666667 6x + x2 = 0 + 18.66666667 Combine like terms: 0 + 18.66666667 = 18.66666667 6x + x2 = 18.66666667 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 = 18.66666667 + 9 Reorder the terms: 9 + 6x + x2 = 18.66666667 + 9 Combine like terms: 18.66666667 + 9 = 27.66666667 9 + 6x + x2 = 27.66666667 Factor a perfect square on the left side: (x + 3)(x + 3) = 27.66666667 Calculate the square root of the right side: 5.25991128 Break this problem into two subproblems by setting (x + 3) equal to 5.25991128 and -5.25991128.Subproblem 1
x + 3 = 5.25991128 Simplifying x + 3 = 5.25991128 Reorder the terms: 3 + x = 5.25991128 Solving 3 + x = 5.25991128 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 = 5.25991128 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5.25991128 + -3 x = 5.25991128 + -3 Combine like terms: 5.25991128 + -3 = 2.25991128 x = 2.25991128 Simplifying x = 2.25991128Subproblem 2
x + 3 = -5.25991128 Simplifying x + 3 = -5.25991128 Reorder the terms: 3 + x = -5.25991128 Solving 3 + x = -5.25991128 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 = -5.25991128 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5.25991128 + -3 x = -5.25991128 + -3 Combine like terms: -5.25991128 + -3 = -8.25991128 x = -8.25991128 Simplifying x = -8.25991128Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.25991128, -8.25991128}
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