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Simplifying 56 = (3x + -13) * 3x Reorder the terms: 56 = (-13 + 3x) * 3x Reorder the terms for easier multiplication: 56 = 3x(-13 + 3x) 56 = (-13 * 3x + 3x * 3x) 56 = (-39x + 9x2) Solving 56 = -39x + 9x2 Solving for variable 'x'. Reorder the terms: 56 + 39x + -9x2 = -39x + 39x + 9x2 + -9x2 Combine like terms: -39x + 39x = 0 56 + 39x + -9x2 = 0 + 9x2 + -9x2 56 + 39x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 56 + 39x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -6.222222222 + -4.333333333x + x2 = 0 Move the constant term to the right: Add '6.222222222' to each side of the equation. -6.222222222 + -4.333333333x + 6.222222222 + x2 = 0 + 6.222222222 Reorder the terms: -6.222222222 + 6.222222222 + -4.333333333x + x2 = 0 + 6.222222222 Combine like terms: -6.222222222 + 6.222222222 = 0.000000000 0.000000000 + -4.333333333x + x2 = 0 + 6.222222222 -4.333333333x + x2 = 0 + 6.222222222 Combine like terms: 0 + 6.222222222 = 6.222222222 -4.333333333x + x2 = 6.222222222 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 = 6.222222222 + 4.694444446 Reorder the terms: 4.694444446 + -4.333333333x + x2 = 6.222222222 + 4.694444446 Combine like terms: 6.222222222 + 4.694444446 = 10.916666668 4.694444446 + -4.333333333x + x2 = 10.916666668 Factor a perfect square on the left side: (x + -2.166666667)(x + -2.166666667) = 10.916666668 Calculate the square root of the right side: 3.304037934 Break this problem into two subproblems by setting (x + -2.166666667) equal to 3.304037934 and -3.304037934.Subproblem 1
x + -2.166666667 = 3.304037934 Simplifying x + -2.166666667 = 3.304037934 Reorder the terms: -2.166666667 + x = 3.304037934 Solving -2.166666667 + x = 3.304037934 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 = 3.304037934 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = 3.304037934 + 2.166666667 x = 3.304037934 + 2.166666667 Combine like terms: 3.304037934 + 2.166666667 = 5.470704601 x = 5.470704601 Simplifying x = 5.470704601Subproblem 2
x + -2.166666667 = -3.304037934 Simplifying x + -2.166666667 = -3.304037934 Reorder the terms: -2.166666667 + x = -3.304037934 Solving -2.166666667 + x = -3.304037934 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 = -3.304037934 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = -3.304037934 + 2.166666667 x = -3.304037934 + 2.166666667 Combine like terms: -3.304037934 + 2.166666667 = -1.137371267 x = -1.137371267 Simplifying x = -1.137371267Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.470704601, -1.137371267}
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