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Simplifying 3x2 + 45x + -168 = 0 Reorder the terms: -168 + 45x + 3x2 = 0 Solving -168 + 45x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-56 + 15x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-56 + 15x + x2)' equal to zero and attempt to solve: Simplifying -56 + 15x + x2 = 0 Solving -56 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + 15x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + 15x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + 15x + x2 = 0 + 56 15x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 15x + x2 = 56 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 56 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 56 + 56.25 Combine like terms: 56 + 56.25 = 112.25 56.25 + 15x + x2 = 112.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 112.25 Calculate the square root of the right side: 10.59481005 Break this problem into two subproblems by setting (x + 7.5) equal to 10.59481005 and -10.59481005.Subproblem 1
x + 7.5 = 10.59481005 Simplifying x + 7.5 = 10.59481005 Reorder the terms: 7.5 + x = 10.59481005 Solving 7.5 + x = 10.59481005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 10.59481005 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 10.59481005 + -7.5 x = 10.59481005 + -7.5 Combine like terms: 10.59481005 + -7.5 = 3.09481005 x = 3.09481005 Simplifying x = 3.09481005Subproblem 2
x + 7.5 = -10.59481005 Simplifying x + 7.5 = -10.59481005 Reorder the terms: 7.5 + x = -10.59481005 Solving 7.5 + x = -10.59481005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -10.59481005 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -10.59481005 + -7.5 x = -10.59481005 + -7.5 Combine like terms: -10.59481005 + -7.5 = -18.09481005 x = -18.09481005 Simplifying x = -18.09481005Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.09481005, -18.09481005}Solution
x = {3.09481005, -18.09481005}
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