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Simplifying 3x2 + -84x + 6 = 0 Reorder the terms: 6 + -84x + 3x2 = 0 Solving 6 + -84x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(2 + -28x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + -28x + x2)' equal to zero and attempt to solve: Simplifying 2 + -28x + x2 = 0 Solving 2 + -28x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -28x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -28x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -28x + x2 = 0 + -2 -28x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -28x + x2 = -2 The x term is -28x. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x + 196 + x2 = -2 + 196 Reorder the terms: 196 + -28x + x2 = -2 + 196 Combine like terms: -2 + 196 = 194 196 + -28x + x2 = 194 Factor a perfect square on the left side: (x + -14)(x + -14) = 194 Calculate the square root of the right side: 13.928388277 Break this problem into two subproblems by setting (x + -14) equal to 13.928388277 and -13.928388277.Subproblem 1
x + -14 = 13.928388277 Simplifying x + -14 = 13.928388277 Reorder the terms: -14 + x = 13.928388277 Solving -14 + x = 13.928388277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 13.928388277 + 14 Combine like terms: -14 + 14 = 0 0 + x = 13.928388277 + 14 x = 13.928388277 + 14 Combine like terms: 13.928388277 + 14 = 27.928388277 x = 27.928388277 Simplifying x = 27.928388277Subproblem 2
x + -14 = -13.928388277 Simplifying x + -14 = -13.928388277 Reorder the terms: -14 + x = -13.928388277 Solving -14 + x = -13.928388277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -13.928388277 + 14 Combine like terms: -14 + 14 = 0 0 + x = -13.928388277 + 14 x = -13.928388277 + 14 Combine like terms: -13.928388277 + 14 = 0.071611723 x = 0.071611723 Simplifying x = 0.071611723Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.928388277, 0.071611723}Solution
x = {27.928388277, 0.071611723}
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