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Simplifying 3x2 + 13x = 18 Reorder the terms: 13x + 3x2 = 18 Solving 13x + 3x2 = 18 Solving for variable 'x'. Reorder the terms: -18 + 13x + 3x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 13x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6 + 4.333333333x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 4.333333333x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 4.333333333x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 4.333333333x + x2 = 0 + 6 4.333333333x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 4.333333333x + x2 = 6 The x term is 4.333333333x. Take half its coefficient (2.166666667). Square it (4.694444446) and add it to both sides. Add '4.694444446' to each side of the equation. 4.333333333x + 4.694444446 + x2 = 6 + 4.694444446 Reorder the terms: 4.694444446 + 4.333333333x + x2 = 6 + 4.694444446 Combine like terms: 6 + 4.694444446 = 10.694444446 4.694444446 + 4.333333333x + x2 = 10.694444446 Factor a perfect square on the left side: (x + 2.166666667)(x + 2.166666667) = 10.694444446 Calculate the square root of the right side: 3.270236145 Break this problem into two subproblems by setting (x + 2.166666667) equal to 3.270236145 and -3.270236145.Subproblem 1
x + 2.166666667 = 3.270236145 Simplifying x + 2.166666667 = 3.270236145 Reorder the terms: 2.166666667 + x = 3.270236145 Solving 2.166666667 + x = 3.270236145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + x = 3.270236145 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = 3.270236145 + -2.166666667 x = 3.270236145 + -2.166666667 Combine like terms: 3.270236145 + -2.166666667 = 1.103569478 x = 1.103569478 Simplifying x = 1.103569478Subproblem 2
x + 2.166666667 = -3.270236145 Simplifying x + 2.166666667 = -3.270236145 Reorder the terms: 2.166666667 + x = -3.270236145 Solving 2.166666667 + x = -3.270236145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + x = -3.270236145 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = -3.270236145 + -2.166666667 x = -3.270236145 + -2.166666667 Combine like terms: -3.270236145 + -2.166666667 = -5.436902812 x = -5.436902812 Simplifying x = -5.436902812Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.103569478, -5.436902812}
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