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Simplifying 32x2 + 66x + -4 = 0 Reorder the terms: -4 + 66x + 32x2 = 0 Solving -4 + 66x + 32x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 33x + 16x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 33x + 16x2)' equal to zero and attempt to solve: Simplifying -2 + 33x + 16x2 = 0 Solving -2 + 33x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.125 + 2.0625x + x2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + 2.0625x + 0.125 + x2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + 2.0625x + x2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + 2.0625x + x2 = 0 + 0.125 2.0625x + x2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 2.0625x + x2 = 0.125 The x term is 2.0625x. Take half its coefficient (1.03125). Square it (1.063476563) and add it to both sides. Add '1.063476563' to each side of the equation. 2.0625x + 1.063476563 + x2 = 0.125 + 1.063476563 Reorder the terms: 1.063476563 + 2.0625x + x2 = 0.125 + 1.063476563 Combine like terms: 0.125 + 1.063476563 = 1.188476563 1.063476563 + 2.0625x + x2 = 1.188476563 Factor a perfect square on the left side: (x + 1.03125)(x + 1.03125) = 1.188476563 Calculate the square root of the right side: 1.090172722 Break this problem into two subproblems by setting (x + 1.03125) equal to 1.090172722 and -1.090172722.Subproblem 1
x + 1.03125 = 1.090172722 Simplifying x + 1.03125 = 1.090172722 Reorder the terms: 1.03125 + x = 1.090172722 Solving 1.03125 + x = 1.090172722 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.03125' to each side of the equation. 1.03125 + -1.03125 + x = 1.090172722 + -1.03125 Combine like terms: 1.03125 + -1.03125 = 0.00000 0.00000 + x = 1.090172722 + -1.03125 x = 1.090172722 + -1.03125 Combine like terms: 1.090172722 + -1.03125 = 0.058922722 x = 0.058922722 Simplifying x = 0.058922722Subproblem 2
x + 1.03125 = -1.090172722 Simplifying x + 1.03125 = -1.090172722 Reorder the terms: 1.03125 + x = -1.090172722 Solving 1.03125 + x = -1.090172722 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.03125' to each side of the equation. 1.03125 + -1.03125 + x = -1.090172722 + -1.03125 Combine like terms: 1.03125 + -1.03125 = 0.00000 0.00000 + x = -1.090172722 + -1.03125 x = -1.090172722 + -1.03125 Combine like terms: -1.090172722 + -1.03125 = -2.121422722 x = -2.121422722 Simplifying x = -2.121422722Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.058922722, -2.121422722}Solution
x = {0.058922722, -2.121422722}
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