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Simplifying 4x2 + -36x + 64 = 0 Reorder the terms: 64 + -36x + 4x2 = 0 Solving 64 + -36x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(16 + -9x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(16 + -9x + x2)' equal to zero and attempt to solve: Simplifying 16 + -9x + x2 = 0 Solving 16 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + -9x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + -9x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -9x + x2 = 0 + -16 -9x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -9x + x2 = -16 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -16 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -16 + 20.25 Combine like terms: -16 + 20.25 = 4.25 20.25 + -9x + x2 = 4.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + -4.5) equal to 2.061552813 and -2.061552813.Subproblem 1
x + -4.5 = 2.061552813 Simplifying x + -4.5 = 2.061552813 Reorder the terms: -4.5 + x = 2.061552813 Solving -4.5 + x = 2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 2.061552813 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 2.061552813 + 4.5 x = 2.061552813 + 4.5 Combine like terms: 2.061552813 + 4.5 = 6.561552813 x = 6.561552813 Simplifying x = 6.561552813Subproblem 2
x + -4.5 = -2.061552813 Simplifying x + -4.5 = -2.061552813 Reorder the terms: -4.5 + x = -2.061552813 Solving -4.5 + x = -2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -2.061552813 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -2.061552813 + 4.5 x = -2.061552813 + 4.5 Combine like terms: -2.061552813 + 4.5 = 2.438447187 x = 2.438447187 Simplifying x = 2.438447187Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.561552813, 2.438447187}Solution
x = {6.561552813, 2.438447187}
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