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Simplifying 0 = 6x2 + -48x + 54 Reorder the terms: 0 = 54 + -48x + 6x2 Solving 0 = 54 + -48x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -54 = -54 -54 + 48x + -6x2 = 54 + -48x + 6x2 + -54 + 48x + -6x2 Reorder the terms: -54 + 48x + -6x2 = 54 + -54 + -48x + 48x + 6x2 + -6x2 Combine like terms: 54 + -54 = 0 -54 + 48x + -6x2 = 0 + -48x + 48x + 6x2 + -6x2 -54 + 48x + -6x2 = -48x + 48x + 6x2 + -6x2 Combine like terms: -48x + 48x = 0 -54 + 48x + -6x2 = 0 + 6x2 + -6x2 -54 + 48x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -54 + 48x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-9 + 8x + -1x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-9 + 8x + -1x2)' equal to zero and attempt to solve: Simplifying -9 + 8x + -1x2 = 0 Solving -9 + 8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 9 + -8x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -8x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -8x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -8x + x2 = 0 + -9 -8x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -8x + x2 = -9 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 = -9 + 16 Reorder the terms: 16 + -8x + x2 = -9 + 16 Combine like terms: -9 + 16 = 7 16 + -8x + x2 = 7 Factor a perfect square on the left side: (x + -4)(x + -4) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + -4) equal to 2.645751311 and -2.645751311.Subproblem 1
x + -4 = 2.645751311 Simplifying x + -4 = 2.645751311 Reorder the terms: -4 + x = 2.645751311 Solving -4 + x = 2.645751311 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 = 2.645751311 + 4 Combine like terms: -4 + 4 = 0 0 + x = 2.645751311 + 4 x = 2.645751311 + 4 Combine like terms: 2.645751311 + 4 = 6.645751311 x = 6.645751311 Simplifying x = 6.645751311Subproblem 2
x + -4 = -2.645751311 Simplifying x + -4 = -2.645751311 Reorder the terms: -4 + x = -2.645751311 Solving -4 + x = -2.645751311 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 = -2.645751311 + 4 Combine like terms: -4 + 4 = 0 0 + x = -2.645751311 + 4 x = -2.645751311 + 4 Combine like terms: -2.645751311 + 4 = 1.354248689 x = 1.354248689 Simplifying x = 1.354248689Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.645751311, 1.354248689}Solution
x = {6.645751311, 1.354248689}
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