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Simplifying -16x2 + 122x + 6 = 0 Reorder the terms: 6 + 122x + -16x2 = 0 Solving 6 + 122x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 61x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 61x + -8x2)' equal to zero and attempt to solve: Simplifying 3 + 61x + -8x2 = 0 Solving 3 + 61x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.375 + -7.625x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -7.625x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -7.625x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -7.625x + x2 = 0 + 0.375 -7.625x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -7.625x + x2 = 0.375 The x term is -7.625x. Take half its coefficient (-3.8125). Square it (14.53515625) and add it to both sides. Add '14.53515625' to each side of the equation. -7.625x + 14.53515625 + x2 = 0.375 + 14.53515625 Reorder the terms: 14.53515625 + -7.625x + x2 = 0.375 + 14.53515625 Combine like terms: 0.375 + 14.53515625 = 14.91015625 14.53515625 + -7.625x + x2 = 14.91015625 Factor a perfect square on the left side: (x + -3.8125)(x + -3.8125) = 14.91015625 Calculate the square root of the right side: 3.861367148 Break this problem into two subproblems by setting (x + -3.8125) equal to 3.861367148 and -3.861367148.Subproblem 1
x + -3.8125 = 3.861367148 Simplifying x + -3.8125 = 3.861367148 Reorder the terms: -3.8125 + x = 3.861367148 Solving -3.8125 + x = 3.861367148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.8125' to each side of the equation. -3.8125 + 3.8125 + x = 3.861367148 + 3.8125 Combine like terms: -3.8125 + 3.8125 = 0.0000 0.0000 + x = 3.861367148 + 3.8125 x = 3.861367148 + 3.8125 Combine like terms: 3.861367148 + 3.8125 = 7.673867148 x = 7.673867148 Simplifying x = 7.673867148Subproblem 2
x + -3.8125 = -3.861367148 Simplifying x + -3.8125 = -3.861367148 Reorder the terms: -3.8125 + x = -3.861367148 Solving -3.8125 + x = -3.861367148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.8125' to each side of the equation. -3.8125 + 3.8125 + x = -3.861367148 + 3.8125 Combine like terms: -3.8125 + 3.8125 = 0.0000 0.0000 + x = -3.861367148 + 3.8125 x = -3.861367148 + 3.8125 Combine like terms: -3.861367148 + 3.8125 = -0.048867148 x = -0.048867148 Simplifying x = -0.048867148Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.673867148, -0.048867148}Solution
x = {7.673867148, -0.048867148}
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