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Simplifying -16x2 + -32x + 320 = 64 Reorder the terms: 320 + -32x + -16x2 = 64 Solving 320 + -32x + -16x2 = 64 Solving for variable 'x'. Reorder the terms: 320 + -64 + -32x + -16x2 = 64 + -64 Combine like terms: 320 + -64 = 256 256 + -32x + -16x2 = 64 + -64 Combine like terms: 64 + -64 = 0 256 + -32x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(16 + -2x + -1x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(16 + -2x + -1x2)' equal to zero and attempt to solve: Simplifying 16 + -2x + -1x2 = 0 Solving 16 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -16 + 2x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 2x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 2x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 2x + x2 = 0 + 16 2x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 2x + x2 = 16 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 16 + 1 Reorder the terms: 1 + 2x + x2 = 16 + 1 Combine like terms: 16 + 1 = 17 1 + 2x + x2 = 17 Factor a perfect square on the left side: (x + 1)(x + 1) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x + 1) equal to 4.123105626 and -4.123105626.Subproblem 1
x + 1 = 4.123105626 Simplifying x + 1 = 4.123105626 Reorder the terms: 1 + x = 4.123105626 Solving 1 + x = 4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 4.123105626 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.123105626 + -1 x = 4.123105626 + -1 Combine like terms: 4.123105626 + -1 = 3.123105626 x = 3.123105626 Simplifying x = 3.123105626Subproblem 2
x + 1 = -4.123105626 Simplifying x + 1 = -4.123105626 Reorder the terms: 1 + x = -4.123105626 Solving 1 + x = -4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -4.123105626 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.123105626 + -1 x = -4.123105626 + -1 Combine like terms: -4.123105626 + -1 = -5.123105626 x = -5.123105626 Simplifying x = -5.123105626Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.123105626, -5.123105626}Solution
x = {3.123105626, -5.123105626}
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