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Simplifying 16x = 2x2 + 16 Reorder the terms: 16x = 16 + 2x2 Solving 16x = 16 + 2x2 Solving for variable 'x'. Reorder the terms: -16 + 16x + -2x2 = 16 + 2x2 + -16 + -2x2 Reorder the terms: -16 + 16x + -2x2 = 16 + -16 + 2x2 + -2x2 Combine like terms: 16 + -16 = 0 -16 + 16x + -2x2 = 0 + 2x2 + -2x2 -16 + 16x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -16 + 16x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 8x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + 8x + -1x2)' equal to zero and attempt to solve: Simplifying -8 + 8x + -1x2 = 0 Solving -8 + 8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 8 + -8x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -8x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -8x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -8x + x2 = 0 + -8 -8x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -8x + x2 = -8 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 = -8 + 16 Reorder the terms: 16 + -8x + x2 = -8 + 16 Combine like terms: -8 + 16 = 8 16 + -8x + x2 = 8 Factor a perfect square on the left side: (x + -4)(x + -4) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + -4) equal to 2.828427125 and -2.828427125.Subproblem 1
x + -4 = 2.828427125 Simplifying x + -4 = 2.828427125 Reorder the terms: -4 + x = 2.828427125 Solving -4 + x = 2.828427125 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 = 2.828427125 + 4 Combine like terms: -4 + 4 = 0 0 + x = 2.828427125 + 4 x = 2.828427125 + 4 Combine like terms: 2.828427125 + 4 = 6.828427125 x = 6.828427125 Simplifying x = 6.828427125Subproblem 2
x + -4 = -2.828427125 Simplifying x + -4 = -2.828427125 Reorder the terms: -4 + x = -2.828427125 Solving -4 + x = -2.828427125 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 = -2.828427125 + 4 Combine like terms: -4 + 4 = 0 0 + x = -2.828427125 + 4 x = -2.828427125 + 4 Combine like terms: -2.828427125 + 4 = 1.171572875 x = 1.171572875 Simplifying x = 1.171572875Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.828427125, 1.171572875}Solution
x = {6.828427125, 1.171572875}
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