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Simplifying 9x2 + 42x = 180 Reorder the terms: 42x + 9x2 = 180 Solving 42x + 9x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 42x + 9x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 42x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-60 + 14x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-60 + 14x + 3x2)' equal to zero and attempt to solve: Simplifying -60 + 14x + 3x2 = 0 Solving -60 + 14x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -20 + 4.666666667x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 4.666666667x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 4.666666667x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 4.666666667x + x2 = 0 + 20 4.666666667x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 4.666666667x + x2 = 20 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 = 20 + 5.444444448 Reorder the terms: 5.444444448 + 4.666666667x + x2 = 20 + 5.444444448 Combine like terms: 20 + 5.444444448 = 25.444444448 5.444444448 + 4.666666667x + x2 = 25.444444448 Factor a perfect square on the left side: (x + 2.333333334)(x + 2.333333334) = 25.444444448 Calculate the square root of the right side: 5.04424865 Break this problem into two subproblems by setting (x + 2.333333334) equal to 5.04424865 and -5.04424865.Subproblem 1
x + 2.333333334 = 5.04424865 Simplifying x + 2.333333334 = 5.04424865 Reorder the terms: 2.333333334 + x = 5.04424865 Solving 2.333333334 + x = 5.04424865 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 = 5.04424865 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = 5.04424865 + -2.333333334 x = 5.04424865 + -2.333333334 Combine like terms: 5.04424865 + -2.333333334 = 2.710915316 x = 2.710915316 Simplifying x = 2.710915316Subproblem 2
x + 2.333333334 = -5.04424865 Simplifying x + 2.333333334 = -5.04424865 Reorder the terms: 2.333333334 + x = -5.04424865 Solving 2.333333334 + x = -5.04424865 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 = -5.04424865 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = -5.04424865 + -2.333333334 x = -5.04424865 + -2.333333334 Combine like terms: -5.04424865 + -2.333333334 = -7.377581984 x = -7.377581984 Simplifying x = -7.377581984Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.710915316, -7.377581984}Solution
x = {2.710915316, -7.377581984}
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