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Simplifying 0 = 2(25 + -54x + -6x2) 0 = (25 * 2 + -54x * 2 + -6x2 * 2) 0 = (50 + -108x + -12x2) Solving 0 = 50 + -108x + -12x2 Solving for variable 'x'. Combine like terms: 0 + -50 = -50 -50 + 108x + 12x2 = 50 + -108x + -12x2 + -50 + 108x + 12x2 Reorder the terms: -50 + 108x + 12x2 = 50 + -50 + -108x + 108x + -12x2 + 12x2 Combine like terms: 50 + -50 = 0 -50 + 108x + 12x2 = 0 + -108x + 108x + -12x2 + 12x2 -50 + 108x + 12x2 = -108x + 108x + -12x2 + 12x2 Combine like terms: -108x + 108x = 0 -50 + 108x + 12x2 = 0 + -12x2 + 12x2 -50 + 108x + 12x2 = -12x2 + 12x2 Combine like terms: -12x2 + 12x2 = 0 -50 + 108x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-25 + 54x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + 54x + 6x2)' equal to zero and attempt to solve: Simplifying -25 + 54x + 6x2 = 0 Solving -25 + 54x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -4.166666667 + 9x + x2 = 0 Move the constant term to the right: Add '4.166666667' to each side of the equation. -4.166666667 + 9x + 4.166666667 + x2 = 0 + 4.166666667 Reorder the terms: -4.166666667 + 4.166666667 + 9x + x2 = 0 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + 9x + x2 = 0 + 4.166666667 9x + x2 = 0 + 4.166666667 Combine like terms: 0 + 4.166666667 = 4.166666667 9x + x2 = 4.166666667 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 4.166666667 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 4.166666667 + 20.25 Combine like terms: 4.166666667 + 20.25 = 24.416666667 20.25 + 9x + x2 = 24.416666667 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 24.416666667 Calculate the square root of the right side: 4.94132236 Break this problem into two subproblems by setting (x + 4.5) equal to 4.94132236 and -4.94132236.Subproblem 1
x + 4.5 = 4.94132236 Simplifying x + 4.5 = 4.94132236 Reorder the terms: 4.5 + x = 4.94132236 Solving 4.5 + x = 4.94132236 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 4.94132236 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 4.94132236 + -4.5 x = 4.94132236 + -4.5 Combine like terms: 4.94132236 + -4.5 = 0.44132236 x = 0.44132236 Simplifying x = 0.44132236Subproblem 2
x + 4.5 = -4.94132236 Simplifying x + 4.5 = -4.94132236 Reorder the terms: 4.5 + x = -4.94132236 Solving 4.5 + x = -4.94132236 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -4.94132236 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -4.94132236 + -4.5 x = -4.94132236 + -4.5 Combine like terms: -4.94132236 + -4.5 = -9.44132236 x = -9.44132236 Simplifying x = -9.44132236Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.44132236, -9.44132236}Solution
x = {0.44132236, -9.44132236}
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