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Simplifying 6x2 + -48x = 9 Reorder the terms: -48x + 6x2 = 9 Solving -48x + 6x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + -48x + 6x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -48x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + -16x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -16x + 2x2)' equal to zero and attempt to solve: Simplifying -3 + -16x + 2x2 = 0 Solving -3 + -16x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + -8x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -8x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -8x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -8x + x2 = 0 + 1.5 -8x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -8x + x2 = 1.5 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 1.5 + 16 Reorder the terms: 16 + -8x + x2 = 1.5 + 16 Combine like terms: 1.5 + 16 = 17.5 16 + -8x + x2 = 17.5 Factor a perfect square on the left side: (x + -4)(x + -4) = 17.5 Calculate the square root of the right side: 4.183300133 Break this problem into two subproblems by setting (x + -4) equal to 4.183300133 and -4.183300133.Subproblem 1
x + -4 = 4.183300133 Simplifying x + -4 = 4.183300133 Reorder the terms: -4 + x = 4.183300133 Solving -4 + x = 4.183300133 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.183300133 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.183300133 + 4 x = 4.183300133 + 4 Combine like terms: 4.183300133 + 4 = 8.183300133 x = 8.183300133 Simplifying x = 8.183300133Subproblem 2
x + -4 = -4.183300133 Simplifying x + -4 = -4.183300133 Reorder the terms: -4 + x = -4.183300133 Solving -4 + x = -4.183300133 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.183300133 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.183300133 + 4 x = -4.183300133 + 4 Combine like terms: -4.183300133 + 4 = -0.183300133 x = -0.183300133 Simplifying x = -0.183300133Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.183300133, -0.183300133}Solution
x = {8.183300133, -0.183300133}
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