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Simplifying 18x + 36 = 3x2 + 4x Reorder the terms: 36 + 18x = 3x2 + 4x Reorder the terms: 36 + 18x = 4x + 3x2 Solving 36 + 18x = 4x + 3x2 Solving for variable 'x'. Combine like terms: 18x + -4x = 14x 36 + 14x + -3x2 = 4x + 3x2 + -4x + -3x2 Reorder the terms: 36 + 14x + -3x2 = 4x + -4x + 3x2 + -3x2 Combine like terms: 4x + -4x = 0 36 + 14x + -3x2 = 0 + 3x2 + -3x2 36 + 14x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 36 + 14x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -12 + -4.666666667x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -4.666666667x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -4.666666667x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -4.666666667x + x2 = 0 + 12 -4.666666667x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -4.666666667x + x2 = 12 The x term is -4.666666667x. Take half its coefficient (-2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. -4.666666667x + 5.444444448 + x2 = 12 + 5.444444448 Reorder the terms: 5.444444448 + -4.666666667x + x2 = 12 + 5.444444448 Combine like terms: 12 + 5.444444448 = 17.444444448 5.444444448 + -4.666666667x + x2 = 17.444444448 Factor a perfect square on the left side: (x + -2.333333334)(x + -2.333333334) = 17.444444448 Calculate the square root of the right side: 4.176654696 Break this problem into two subproblems by setting (x + -2.333333334) equal to 4.176654696 and -4.176654696.Subproblem 1
x + -2.333333334 = 4.176654696 Simplifying x + -2.333333334 = 4.176654696 Reorder the terms: -2.333333334 + x = 4.176654696 Solving -2.333333334 + x = 4.176654696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = 4.176654696 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = 4.176654696 + 2.333333334 x = 4.176654696 + 2.333333334 Combine like terms: 4.176654696 + 2.333333334 = 6.50998803 x = 6.50998803 Simplifying x = 6.50998803Subproblem 2
x + -2.333333334 = -4.176654696 Simplifying x + -2.333333334 = -4.176654696 Reorder the terms: -2.333333334 + x = -4.176654696 Solving -2.333333334 + x = -4.176654696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = -4.176654696 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = -4.176654696 + 2.333333334 x = -4.176654696 + 2.333333334 Combine like terms: -4.176654696 + 2.333333334 = -1.843321362 x = -1.843321362 Simplifying x = -1.843321362Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.50998803, -1.843321362}
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