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Simplifying 8 = 2x2 + 16x Reorder the terms: 8 = 16x + 2x2 Solving 8 = 16x + 2x2 Solving for variable 'x'. Reorder the terms: 8 + -16x + -2x2 = 16x + -16x + 2x2 + -2x2 Combine like terms: 16x + -16x = 0 8 + -16x + -2x2 = 0 + 2x2 + -2x2 8 + -16x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 8 + -16x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -8x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -8x + -1x2)' equal to zero and attempt to solve: Simplifying 4 + -8x + -1x2 = 0 Solving 4 + -8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + 8x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 8x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 8x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 8x + x2 = 0 + 4 8x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 8x + x2 = 4 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 = 4 + 16 Reorder the terms: 16 + 8x + x2 = 4 + 16 Combine like terms: 4 + 16 = 20 16 + 8x + x2 = 20 Factor a perfect square on the left side: (x + 4)(x + 4) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x + 4) equal to 4.472135955 and -4.472135955.Subproblem 1
x + 4 = 4.472135955 Simplifying x + 4 = 4.472135955 Reorder the terms: 4 + x = 4.472135955 Solving 4 + x = 4.472135955 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 = 4.472135955 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.472135955 + -4 x = 4.472135955 + -4 Combine like terms: 4.472135955 + -4 = 0.472135955 x = 0.472135955 Simplifying x = 0.472135955Subproblem 2
x + 4 = -4.472135955 Simplifying x + 4 = -4.472135955 Reorder the terms: 4 + x = -4.472135955 Solving 4 + x = -4.472135955 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 = -4.472135955 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.472135955 + -4 x = -4.472135955 + -4 Combine like terms: -4.472135955 + -4 = -8.472135955 x = -8.472135955 Simplifying x = -8.472135955Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.472135955, -8.472135955}Solution
x = {0.472135955, -8.472135955}
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