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Simplifying 16x2 + -42x + 6 = 0 Reorder the terms: 6 + -42x + 16x2 = 0 Solving 6 + -42x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -21x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -21x + 8x2)' equal to zero and attempt to solve: Simplifying 3 + -21x + 8x2 = 0 Solving 3 + -21x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.375 + -2.625x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + -2.625x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + -2.625x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + -2.625x + x2 = 0 + -0.375 -2.625x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 -2.625x + x2 = -0.375 The x term is -2.625x. Take half its coefficient (-1.3125). Square it (1.72265625) and add it to both sides. Add '1.72265625' to each side of the equation. -2.625x + 1.72265625 + x2 = -0.375 + 1.72265625 Reorder the terms: 1.72265625 + -2.625x + x2 = -0.375 + 1.72265625 Combine like terms: -0.375 + 1.72265625 = 1.34765625 1.72265625 + -2.625x + x2 = 1.34765625 Factor a perfect square on the left side: (x + -1.3125)(x + -1.3125) = 1.34765625 Calculate the square root of the right side: 1.160885976 Break this problem into two subproblems by setting (x + -1.3125) equal to 1.160885976 and -1.160885976.Subproblem 1
x + -1.3125 = 1.160885976 Simplifying x + -1.3125 = 1.160885976 Reorder the terms: -1.3125 + x = 1.160885976 Solving -1.3125 + x = 1.160885976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3125' to each side of the equation. -1.3125 + 1.3125 + x = 1.160885976 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + x = 1.160885976 + 1.3125 x = 1.160885976 + 1.3125 Combine like terms: 1.160885976 + 1.3125 = 2.473385976 x = 2.473385976 Simplifying x = 2.473385976Subproblem 2
x + -1.3125 = -1.160885976 Simplifying x + -1.3125 = -1.160885976 Reorder the terms: -1.3125 + x = -1.160885976 Solving -1.3125 + x = -1.160885976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3125' to each side of the equation. -1.3125 + 1.3125 + x = -1.160885976 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + x = -1.160885976 + 1.3125 x = -1.160885976 + 1.3125 Combine like terms: -1.160885976 + 1.3125 = 0.151614024 x = 0.151614024 Simplifying x = 0.151614024Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.473385976, 0.151614024}Solution
x = {2.473385976, 0.151614024}
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