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Simplifying 4x2 + 8x + 16 = 5832 Reorder the terms: 16 + 8x + 4x2 = 5832 Solving 16 + 8x + 4x2 = 5832 Solving for variable 'x'. Reorder the terms: 16 + -5832 + 8x + 4x2 = 5832 + -5832 Combine like terms: 16 + -5832 = -5816 -5816 + 8x + 4x2 = 5832 + -5832 Combine like terms: 5832 + -5832 = 0 -5816 + 8x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-1454 + 2x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1454 + 2x + x2)' equal to zero and attempt to solve: Simplifying -1454 + 2x + x2 = 0 Solving -1454 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1454' to each side of the equation. -1454 + 2x + 1454 + x2 = 0 + 1454 Reorder the terms: -1454 + 1454 + 2x + x2 = 0 + 1454 Combine like terms: -1454 + 1454 = 0 0 + 2x + x2 = 0 + 1454 2x + x2 = 0 + 1454 Combine like terms: 0 + 1454 = 1454 2x + x2 = 1454 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 = 1454 + 1 Reorder the terms: 1 + 2x + x2 = 1454 + 1 Combine like terms: 1454 + 1 = 1455 1 + 2x + x2 = 1455 Factor a perfect square on the left side: (x + 1)(x + 1) = 1455 Calculate the square root of the right side: 38.144462246 Break this problem into two subproblems by setting (x + 1) equal to 38.144462246 and -38.144462246.Subproblem 1
x + 1 = 38.144462246 Simplifying x + 1 = 38.144462246 Reorder the terms: 1 + x = 38.144462246 Solving 1 + x = 38.144462246 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 = 38.144462246 + -1 Combine like terms: 1 + -1 = 0 0 + x = 38.144462246 + -1 x = 38.144462246 + -1 Combine like terms: 38.144462246 + -1 = 37.144462246 x = 37.144462246 Simplifying x = 37.144462246Subproblem 2
x + 1 = -38.144462246 Simplifying x + 1 = -38.144462246 Reorder the terms: 1 + x = -38.144462246 Solving 1 + x = -38.144462246 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 = -38.144462246 + -1 Combine like terms: 1 + -1 = 0 0 + x = -38.144462246 + -1 x = -38.144462246 + -1 Combine like terms: -38.144462246 + -1 = -39.144462246 x = -39.144462246 Simplifying x = -39.144462246Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.144462246, -39.144462246}Solution
x = {37.144462246, -39.144462246}
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