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Simplifying 48 = 3x2 + 12x Reorder the terms: 48 = 12x + 3x2 Solving 48 = 12x + 3x2 Solving for variable 'x'. Reorder the terms: 48 + -12x + -3x2 = 12x + -12x + 3x2 + -3x2 Combine like terms: 12x + -12x = 0 48 + -12x + -3x2 = 0 + 3x2 + -3x2 48 + -12x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 48 + -12x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(16 + -4x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(16 + -4x + -1x2)' equal to zero and attempt to solve: Simplifying 16 + -4x + -1x2 = 0 Solving 16 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -16 + 4x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 4x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 4x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 4x + x2 = 0 + 16 4x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 4x + x2 = 16 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 16 + 4 Reorder the terms: 4 + 4x + x2 = 16 + 4 Combine like terms: 16 + 4 = 20 4 + 4x + x2 = 20 Factor a perfect square on the left side: (x + 2)(x + 2) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x + 2) equal to 4.472135955 and -4.472135955.Subproblem 1
x + 2 = 4.472135955 Simplifying x + 2 = 4.472135955 Reorder the terms: 2 + x = 4.472135955 Solving 2 + x = 4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 4.472135955 + -2 Combine like terms: 2 + -2 = 0 0 + x = 4.472135955 + -2 x = 4.472135955 + -2 Combine like terms: 4.472135955 + -2 = 2.472135955 x = 2.472135955 Simplifying x = 2.472135955Subproblem 2
x + 2 = -4.472135955 Simplifying x + 2 = -4.472135955 Reorder the terms: 2 + x = -4.472135955 Solving 2 + x = -4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -4.472135955 + -2 Combine like terms: 2 + -2 = 0 0 + x = -4.472135955 + -2 x = -4.472135955 + -2 Combine like terms: -4.472135955 + -2 = -6.472135955 x = -6.472135955 Simplifying x = -6.472135955Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.472135955, -6.472135955}Solution
x = {2.472135955, -6.472135955}
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