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Simplifying 6x2 + 51x + 15 = 0 Reorder the terms: 15 + 51x + 6x2 = 0 Solving 15 + 51x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(5 + 17x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + 17x + 2x2)' equal to zero and attempt to solve: Simplifying 5 + 17x + 2x2 = 0 Solving 5 + 17x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + 8.5x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 8.5x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 8.5x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 8.5x + x2 = 0 + -2.5 8.5x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 8.5x + x2 = -2.5 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 = -2.5 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = -2.5 + 18.0625 Combine like terms: -2.5 + 18.0625 = 15.5625 18.0625 + 8.5x + x2 = 15.5625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 15.5625 Calculate the square root of the right side: 3.94493346 Break this problem into two subproblems by setting (x + 4.25) equal to 3.94493346 and -3.94493346.Subproblem 1
x + 4.25 = 3.94493346 Simplifying x + 4.25 = 3.94493346 Reorder the terms: 4.25 + x = 3.94493346 Solving 4.25 + x = 3.94493346 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 = 3.94493346 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 3.94493346 + -4.25 x = 3.94493346 + -4.25 Combine like terms: 3.94493346 + -4.25 = -0.30506654 x = -0.30506654 Simplifying x = -0.30506654Subproblem 2
x + 4.25 = -3.94493346 Simplifying x + 4.25 = -3.94493346 Reorder the terms: 4.25 + x = -3.94493346 Solving 4.25 + x = -3.94493346 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 = -3.94493346 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -3.94493346 + -4.25 x = -3.94493346 + -4.25 Combine like terms: -3.94493346 + -4.25 = -8.19493346 x = -8.19493346 Simplifying x = -8.19493346Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.30506654, -8.19493346}Solution
x = {-0.30506654, -8.19493346}
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