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Simplifying 50 = 16x2 + 64x + 6 Reorder the terms: 50 = 6 + 64x + 16x2 Solving 50 = 6 + 64x + 16x2 Solving for variable 'x'. Combine like terms: 50 + -6 = 44 44 + -64x + -16x2 = 6 + 64x + 16x2 + -6 + -64x + -16x2 Reorder the terms: 44 + -64x + -16x2 = 6 + -6 + 64x + -64x + 16x2 + -16x2 Combine like terms: 6 + -6 = 0 44 + -64x + -16x2 = 0 + 64x + -64x + 16x2 + -16x2 44 + -64x + -16x2 = 64x + -64x + 16x2 + -16x2 Combine like terms: 64x + -64x = 0 44 + -64x + -16x2 = 0 + 16x2 + -16x2 44 + -64x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 44 + -64x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(11 + -16x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(11 + -16x + -4x2)' equal to zero and attempt to solve: Simplifying 11 + -16x + -4x2 = 0 Solving 11 + -16x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2.75 + 4x + x2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + 4x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + 4x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + 4x + x2 = 0 + 2.75 4x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 4x + x2 = 2.75 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 = 2.75 + 4 Reorder the terms: 4 + 4x + x2 = 2.75 + 4 Combine like terms: 2.75 + 4 = 6.75 4 + 4x + x2 = 6.75 Factor a perfect square on the left side: (x + 2)(x + 2) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (x + 2) equal to 2.598076211 and -2.598076211.Subproblem 1
x + 2 = 2.598076211 Simplifying x + 2 = 2.598076211 Reorder the terms: 2 + x = 2.598076211 Solving 2 + x = 2.598076211 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 = 2.598076211 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.598076211 + -2 x = 2.598076211 + -2 Combine like terms: 2.598076211 + -2 = 0.598076211 x = 0.598076211 Simplifying x = 0.598076211Subproblem 2
x + 2 = -2.598076211 Simplifying x + 2 = -2.598076211 Reorder the terms: 2 + x = -2.598076211 Solving 2 + x = -2.598076211 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 = -2.598076211 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.598076211 + -2 x = -2.598076211 + -2 Combine like terms: -2.598076211 + -2 = -4.598076211 x = -4.598076211 Simplifying x = -4.598076211Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.598076211, -4.598076211}Solution
x = {0.598076211, -4.598076211}
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