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Simplifying 3x2 + 54x + -348 = 0 Reorder the terms: -348 + 54x + 3x2 = 0 Solving -348 + 54x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-116 + 18x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-116 + 18x + x2)' equal to zero and attempt to solve: Simplifying -116 + 18x + x2 = 0 Solving -116 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '116' to each side of the equation. -116 + 18x + 116 + x2 = 0 + 116 Reorder the terms: -116 + 116 + 18x + x2 = 0 + 116 Combine like terms: -116 + 116 = 0 0 + 18x + x2 = 0 + 116 18x + x2 = 0 + 116 Combine like terms: 0 + 116 = 116 18x + x2 = 116 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = 116 + 81 Reorder the terms: 81 + 18x + x2 = 116 + 81 Combine like terms: 116 + 81 = 197 81 + 18x + x2 = 197 Factor a perfect square on the left side: (x + 9)(x + 9) = 197 Calculate the square root of the right side: 14.035668848 Break this problem into two subproblems by setting (x + 9) equal to 14.035668848 and -14.035668848.Subproblem 1
x + 9 = 14.035668848 Simplifying x + 9 = 14.035668848 Reorder the terms: 9 + x = 14.035668848 Solving 9 + x = 14.035668848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 14.035668848 + -9 Combine like terms: 9 + -9 = 0 0 + x = 14.035668848 + -9 x = 14.035668848 + -9 Combine like terms: 14.035668848 + -9 = 5.035668848 x = 5.035668848 Simplifying x = 5.035668848Subproblem 2
x + 9 = -14.035668848 Simplifying x + 9 = -14.035668848 Reorder the terms: 9 + x = -14.035668848 Solving 9 + x = -14.035668848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -14.035668848 + -9 Combine like terms: 9 + -9 = 0 0 + x = -14.035668848 + -9 x = -14.035668848 + -9 Combine like terms: -14.035668848 + -9 = -23.035668848 x = -23.035668848 Simplifying x = -23.035668848Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.035668848, -23.035668848}Solution
x = {5.035668848, -23.035668848}
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