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Simplifying (3x2) + 90x + 324 = 0 Reorder the terms: 324 + 90x + (3x2) = 0 Solving 324 + 90x + (3x2) = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(108 + 30x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(108 + 30x + x2)' equal to zero and attempt to solve: Simplifying 108 + 30x + x2 = 0 Solving 108 + 30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-108' to each side of the equation. 108 + 30x + -108 + x2 = 0 + -108 Reorder the terms: 108 + -108 + 30x + x2 = 0 + -108 Combine like terms: 108 + -108 = 0 0 + 30x + x2 = 0 + -108 30x + x2 = 0 + -108 Combine like terms: 0 + -108 = -108 30x + x2 = -108 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = -108 + 225 Reorder the terms: 225 + 30x + x2 = -108 + 225 Combine like terms: -108 + 225 = 117 225 + 30x + x2 = 117 Factor a perfect square on the left side: (x + 15)(x + 15) = 117 Calculate the square root of the right side: 10.816653826 Break this problem into two subproblems by setting (x + 15) equal to 10.816653826 and -10.816653826.Subproblem 1
x + 15 = 10.816653826 Simplifying x + 15 = 10.816653826 Reorder the terms: 15 + x = 10.816653826 Solving 15 + x = 10.816653826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 10.816653826 + -15 Combine like terms: 15 + -15 = 0 0 + x = 10.816653826 + -15 x = 10.816653826 + -15 Combine like terms: 10.816653826 + -15 = -4.183346174 x = -4.183346174 Simplifying x = -4.183346174Subproblem 2
x + 15 = -10.816653826 Simplifying x + 15 = -10.816653826 Reorder the terms: 15 + x = -10.816653826 Solving 15 + x = -10.816653826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -10.816653826 + -15 Combine like terms: 15 + -15 = 0 0 + x = -10.816653826 + -15 x = -10.816653826 + -15 Combine like terms: -10.816653826 + -15 = -25.816653826 x = -25.816653826 Simplifying x = -25.816653826Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.183346174, -25.816653826}Solution
x = {-4.183346174, -25.816653826}
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