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Simplifying 6x2 + 51x = 21 Reorder the terms: 51x + 6x2 = 21 Solving 51x + 6x2 = 21 Solving for variable 'x'. Reorder the terms: -21 + 51x + 6x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + 51x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-7 + 17x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + 17x + 2x2)' equal to zero and attempt to solve: Simplifying -7 + 17x + 2x2 = 0 Solving -7 + 17x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 8.5x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 8.5x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 8.5x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 8.5x + x2 = 0 + 3.5 8.5x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 8.5x + x2 = 3.5 The x term is 8.5x. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5x + 18.0625 + x2 = 3.5 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = 3.5 + 18.0625 Combine like terms: 3.5 + 18.0625 = 21.5625 18.0625 + 8.5x + x2 = 21.5625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 21.5625 Calculate the square root of the right side: 4.643543905 Break this problem into two subproblems by setting (x + 4.25) equal to 4.643543905 and -4.643543905.Subproblem 1
x + 4.25 = 4.643543905 Simplifying x + 4.25 = 4.643543905 Reorder the terms: 4.25 + x = 4.643543905 Solving 4.25 + x = 4.643543905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 4.643543905 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 4.643543905 + -4.25 x = 4.643543905 + -4.25 Combine like terms: 4.643543905 + -4.25 = 0.393543905 x = 0.393543905 Simplifying x = 0.393543905Subproblem 2
x + 4.25 = -4.643543905 Simplifying x + 4.25 = -4.643543905 Reorder the terms: 4.25 + x = -4.643543905 Solving 4.25 + x = -4.643543905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -4.643543905 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -4.643543905 + -4.25 x = -4.643543905 + -4.25 Combine like terms: -4.643543905 + -4.25 = -8.893543905 x = -8.893543905 Simplifying x = -8.893543905Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.393543905, -8.893543905}Solution
x = {0.393543905, -8.893543905}
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