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Simplifying 4(x2 + 64x + -288) = 0 Reorder the terms: 4(-288 + 64x + x2) = 0 (-288 * 4 + 64x * 4 + x2 * 4) = 0 (-1152 + 256x + 4x2) = 0 Solving -1152 + 256x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-288 + 64x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-288 + 64x + x2)' equal to zero and attempt to solve: Simplifying -288 + 64x + x2 = 0 Solving -288 + 64x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '288' to each side of the equation. -288 + 64x + 288 + x2 = 0 + 288 Reorder the terms: -288 + 288 + 64x + x2 = 0 + 288 Combine like terms: -288 + 288 = 0 0 + 64x + x2 = 0 + 288 64x + x2 = 0 + 288 Combine like terms: 0 + 288 = 288 64x + x2 = 288 The x term is 64x. Take half its coefficient (32). Square it (1024) and add it to both sides. Add '1024' to each side of the equation. 64x + 1024 + x2 = 288 + 1024 Reorder the terms: 1024 + 64x + x2 = 288 + 1024 Combine like terms: 288 + 1024 = 1312 1024 + 64x + x2 = 1312 Factor a perfect square on the left side: (x + 32)(x + 32) = 1312 Calculate the square root of the right side: 36.221540553 Break this problem into two subproblems by setting (x + 32) equal to 36.221540553 and -36.221540553.Subproblem 1
x + 32 = 36.221540553 Simplifying x + 32 = 36.221540553 Reorder the terms: 32 + x = 36.221540553 Solving 32 + x = 36.221540553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + x = 36.221540553 + -32 Combine like terms: 32 + -32 = 0 0 + x = 36.221540553 + -32 x = 36.221540553 + -32 Combine like terms: 36.221540553 + -32 = 4.221540553 x = 4.221540553 Simplifying x = 4.221540553Subproblem 2
x + 32 = -36.221540553 Simplifying x + 32 = -36.221540553 Reorder the terms: 32 + x = -36.221540553 Solving 32 + x = -36.221540553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + x = -36.221540553 + -32 Combine like terms: 32 + -32 = 0 0 + x = -36.221540553 + -32 x = -36.221540553 + -32 Combine like terms: -36.221540553 + -32 = -68.221540553 x = -68.221540553 Simplifying x = -68.221540553Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.221540553, -68.221540553}Solution
x = {4.221540553, -68.221540553}
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