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Simplifying 3x2 + -54x + 84 = 0 Reorder the terms: 84 + -54x + 3x2 = 0 Solving 84 + -54x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(28 + -18x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(28 + -18x + x2)' equal to zero and attempt to solve: Simplifying 28 + -18x + x2 = 0 Solving 28 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + -18x + -28 + x2 = 0 + -28 Reorder the terms: 28 + -28 + -18x + x2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -18x + x2 = 0 + -28 -18x + x2 = 0 + -28 Combine like terms: 0 + -28 = -28 -18x + x2 = -28 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 = -28 + 81 Reorder the terms: 81 + -18x + x2 = -28 + 81 Combine like terms: -28 + 81 = 53 81 + -18x + x2 = 53 Factor a perfect square on the left side: (x + -9)(x + -9) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (x + -9) equal to 7.280109889 and -7.280109889.Subproblem 1
x + -9 = 7.280109889 Simplifying x + -9 = 7.280109889 Reorder the terms: -9 + x = 7.280109889 Solving -9 + x = 7.280109889 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 = 7.280109889 + 9 Combine like terms: -9 + 9 = 0 0 + x = 7.280109889 + 9 x = 7.280109889 + 9 Combine like terms: 7.280109889 + 9 = 16.280109889 x = 16.280109889 Simplifying x = 16.280109889Subproblem 2
x + -9 = -7.280109889 Simplifying x + -9 = -7.280109889 Reorder the terms: -9 + x = -7.280109889 Solving -9 + x = -7.280109889 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 = -7.280109889 + 9 Combine like terms: -9 + 9 = 0 0 + x = -7.280109889 + 9 x = -7.280109889 + 9 Combine like terms: -7.280109889 + 9 = 1.719890111 x = 1.719890111 Simplifying x = 1.719890111Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.280109889, 1.719890111}Solution
x = {16.280109889, 1.719890111}
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