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Simplifying 30 + -1x = 3x(x + 6) Reorder the terms: 30 + -1x = 3x(6 + x) 30 + -1x = (6 * 3x + x * 3x) 30 + -1x = (18x + 3x2) Solving 30 + -1x = 18x + 3x2 Solving for variable 'x'. Combine like terms: -1x + -18x = -19x 30 + -19x + -3x2 = 18x + 3x2 + -18x + -3x2 Reorder the terms: 30 + -19x + -3x2 = 18x + -18x + 3x2 + -3x2 Combine like terms: 18x + -18x = 0 30 + -19x + -3x2 = 0 + 3x2 + -3x2 30 + -19x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 30 + -19x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -10 + 6.333333333x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 6.333333333x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 6.333333333x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 6.333333333x + x2 = 0 + 10 6.333333333x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 6.333333333x + x2 = 10 The x term is 6.333333333x. Take half its coefficient (3.166666667). Square it (10.02777778) and add it to both sides. Add '10.02777778' to each side of the equation. 6.333333333x + 10.02777778 + x2 = 10 + 10.02777778 Reorder the terms: 10.02777778 + 6.333333333x + x2 = 10 + 10.02777778 Combine like terms: 10 + 10.02777778 = 20.02777778 10.02777778 + 6.333333333x + x2 = 20.02777778 Factor a perfect square on the left side: (x + 3.166666667)(x + 3.166666667) = 20.02777778 Calculate the square root of the right side: 4.475240528 Break this problem into two subproblems by setting (x + 3.166666667) equal to 4.475240528 and -4.475240528.Subproblem 1
x + 3.166666667 = 4.475240528 Simplifying x + 3.166666667 = 4.475240528 Reorder the terms: 3.166666667 + x = 4.475240528 Solving 3.166666667 + x = 4.475240528 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.166666667' to each side of the equation. 3.166666667 + -3.166666667 + x = 4.475240528 + -3.166666667 Combine like terms: 3.166666667 + -3.166666667 = 0.000000000 0.000000000 + x = 4.475240528 + -3.166666667 x = 4.475240528 + -3.166666667 Combine like terms: 4.475240528 + -3.166666667 = 1.308573861 x = 1.308573861 Simplifying x = 1.308573861Subproblem 2
x + 3.166666667 = -4.475240528 Simplifying x + 3.166666667 = -4.475240528 Reorder the terms: 3.166666667 + x = -4.475240528 Solving 3.166666667 + x = -4.475240528 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.166666667' to each side of the equation. 3.166666667 + -3.166666667 + x = -4.475240528 + -3.166666667 Combine like terms: 3.166666667 + -3.166666667 = 0.000000000 0.000000000 + x = -4.475240528 + -3.166666667 x = -4.475240528 + -3.166666667 Combine like terms: -4.475240528 + -3.166666667 = -7.641907195 x = -7.641907195 Simplifying x = -7.641907195Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.308573861, -7.641907195}
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