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Simplifying 16x2 + -150x + 102 = 0 Reorder the terms: 102 + -150x + 16x2 = 0 Solving 102 + -150x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(51 + -75x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(51 + -75x + 8x2)' equal to zero and attempt to solve: Simplifying 51 + -75x + 8x2 = 0 Solving 51 + -75x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 6.375 + -9.375x + x2 = 0 Move the constant term to the right: Add '-6.375' to each side of the equation. 6.375 + -9.375x + -6.375 + x2 = 0 + -6.375 Reorder the terms: 6.375 + -6.375 + -9.375x + x2 = 0 + -6.375 Combine like terms: 6.375 + -6.375 = 0.000 0.000 + -9.375x + x2 = 0 + -6.375 -9.375x + x2 = 0 + -6.375 Combine like terms: 0 + -6.375 = -6.375 -9.375x + x2 = -6.375 The x term is -9.375x. Take half its coefficient (-4.6875). Square it (21.97265625) and add it to both sides. Add '21.97265625' to each side of the equation. -9.375x + 21.97265625 + x2 = -6.375 + 21.97265625 Reorder the terms: 21.97265625 + -9.375x + x2 = -6.375 + 21.97265625 Combine like terms: -6.375 + 21.97265625 = 15.59765625 21.97265625 + -9.375x + x2 = 15.59765625 Factor a perfect square on the left side: (x + -4.6875)(x + -4.6875) = 15.59765625 Calculate the square root of the right side: 3.949386819 Break this problem into two subproblems by setting (x + -4.6875) equal to 3.949386819 and -3.949386819.Subproblem 1
x + -4.6875 = 3.949386819 Simplifying x + -4.6875 = 3.949386819 Reorder the terms: -4.6875 + x = 3.949386819 Solving -4.6875 + x = 3.949386819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.6875' to each side of the equation. -4.6875 + 4.6875 + x = 3.949386819 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + x = 3.949386819 + 4.6875 x = 3.949386819 + 4.6875 Combine like terms: 3.949386819 + 4.6875 = 8.636886819 x = 8.636886819 Simplifying x = 8.636886819Subproblem 2
x + -4.6875 = -3.949386819 Simplifying x + -4.6875 = -3.949386819 Reorder the terms: -4.6875 + x = -3.949386819 Solving -4.6875 + x = -3.949386819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.6875' to each side of the equation. -4.6875 + 4.6875 + x = -3.949386819 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + x = -3.949386819 + 4.6875 x = -3.949386819 + 4.6875 Combine like terms: -3.949386819 + 4.6875 = 0.738113181 x = 0.738113181 Simplifying x = 0.738113181Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.636886819, 0.738113181}Solution
x = {8.636886819, 0.738113181}
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