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Simplifying 48 = 16x2 + 64x Reorder the terms: 48 = 64x + 16x2 Solving 48 = 64x + 16x2 Solving for variable 'x'. Reorder the terms: 48 + -64x + -16x2 = 64x + -64x + 16x2 + -16x2 Combine like terms: 64x + -64x = 0 48 + -64x + -16x2 = 0 + 16x2 + -16x2 48 + -64x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 48 + -64x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(3 + -4x + -1x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(3 + -4x + -1x2)' equal to zero and attempt to solve: Simplifying 3 + -4x + -1x2 = 0 Solving 3 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + 4x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 4x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 4x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4x + x2 = 0 + 3 4x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 4x + x2 = 3 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 = 3 + 4 Reorder the terms: 4 + 4x + x2 = 3 + 4 Combine like terms: 3 + 4 = 7 4 + 4x + x2 = 7 Factor a perfect square on the left side: (x + 2)(x + 2) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + 2) equal to 2.645751311 and -2.645751311.Subproblem 1
x + 2 = 2.645751311 Simplifying x + 2 = 2.645751311 Reorder the terms: 2 + x = 2.645751311 Solving 2 + x = 2.645751311 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 = 2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.645751311 + -2 x = 2.645751311 + -2 Combine like terms: 2.645751311 + -2 = 0.645751311 x = 0.645751311 Simplifying x = 0.645751311Subproblem 2
x + 2 = -2.645751311 Simplifying x + 2 = -2.645751311 Reorder the terms: 2 + x = -2.645751311 Solving 2 + x = -2.645751311 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 = -2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.645751311 + -2 x = -2.645751311 + -2 Combine like terms: -2.645751311 + -2 = -4.645751311 x = -4.645751311 Simplifying x = -4.645751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.645751311, -4.645751311}Solution
x = {0.645751311, -4.645751311}
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