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Simplifying 64x2 + -72x + 2 = 0 Reorder the terms: 2 + -72x + 64x2 = 0 Solving 2 + -72x + 64x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -36x + 32x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -36x + 32x2)' equal to zero and attempt to solve: Simplifying 1 + -36x + 32x2 = 0 Solving 1 + -36x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. 0.03125 + -1.125x + x2 = 0 Move the constant term to the right: Add '-0.03125' to each side of the equation. 0.03125 + -1.125x + -0.03125 + x2 = 0 + -0.03125 Reorder the terms: 0.03125 + -0.03125 + -1.125x + x2 = 0 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + -1.125x + x2 = 0 + -0.03125 -1.125x + x2 = 0 + -0.03125 Combine like terms: 0 + -0.03125 = -0.03125 -1.125x + x2 = -0.03125 The x term is -1.125x. Take half its coefficient (-0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. -1.125x + 0.31640625 + x2 = -0.03125 + 0.31640625 Reorder the terms: 0.31640625 + -1.125x + x2 = -0.03125 + 0.31640625 Combine like terms: -0.03125 + 0.31640625 = 0.28515625 0.31640625 + -1.125x + x2 = 0.28515625 Factor a perfect square on the left side: (x + -0.5625)(x + -0.5625) = 0.28515625 Calculate the square root of the right side: 0.534000234 Break this problem into two subproblems by setting (x + -0.5625) equal to 0.534000234 and -0.534000234.Subproblem 1
x + -0.5625 = 0.534000234 Simplifying x + -0.5625 = 0.534000234 Reorder the terms: -0.5625 + x = 0.534000234 Solving -0.5625 + x = 0.534000234 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = 0.534000234 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = 0.534000234 + 0.5625 x = 0.534000234 + 0.5625 Combine like terms: 0.534000234 + 0.5625 = 1.096500234 x = 1.096500234 Simplifying x = 1.096500234Subproblem 2
x + -0.5625 = -0.534000234 Simplifying x + -0.5625 = -0.534000234 Reorder the terms: -0.5625 + x = -0.534000234 Solving -0.5625 + x = -0.534000234 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = -0.534000234 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = -0.534000234 + 0.5625 x = -0.534000234 + 0.5625 Combine like terms: -0.534000234 + 0.5625 = 0.028499766 x = 0.028499766 Simplifying x = 0.028499766Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.096500234, 0.028499766}Solution
x = {1.096500234, 0.028499766}
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