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Simplifying 2x4 + -76x2 + 18 = 0 Reorder the terms: 18 + -76x2 + 2x4 = 0 Solving 18 + -76x2 + 2x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + -38x2 + x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -38x2 + x4)' equal to zero and attempt to solve: Simplifying 9 + -38x2 + x4 = 0 Solving 9 + -38x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -38x2 + -9 + x4 = 0 + -9 Reorder the terms: 9 + -9 + -38x2 + x4 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -38x2 + x4 = 0 + -9 -38x2 + x4 = 0 + -9 Combine like terms: 0 + -9 = -9 -38x2 + x4 = -9 The x term is -38x2. Take half its coefficient (-19). Square it (361) and add it to both sides. Add '361' to each side of the equation. -38x2 + 361 + x4 = -9 + 361 Reorder the terms: 361 + -38x2 + x4 = -9 + 361 Combine like terms: -9 + 361 = 352 361 + -38x2 + x4 = 352 Factor a perfect square on the left side: (x2 + -19)(x2 + -19) = 352 Calculate the square root of the right side: 18.761663039 Break this problem into two subproblems by setting (x2 + -19) equal to 18.761663039 and -18.761663039.Subproblem 1
x2 + -19 = 18.761663039 Simplifying x2 + -19 = 18.761663039 Reorder the terms: -19 + x2 = 18.761663039 Solving -19 + x2 = 18.761663039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x2 = 18.761663039 + 19 Combine like terms: -19 + 19 = 0 0 + x2 = 18.761663039 + 19 x2 = 18.761663039 + 19 Combine like terms: 18.761663039 + 19 = 37.761663039 x2 = 37.761663039 Simplifying x2 = 37.761663039 Take the square root of each side: x = {-6.145051915, 6.145051915}Subproblem 2
x2 + -19 = -18.761663039 Simplifying x2 + -19 = -18.761663039 Reorder the terms: -19 + x2 = -18.761663039 Solving -19 + x2 = -18.761663039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x2 = -18.761663039 + 19 Combine like terms: -19 + 19 = 0 0 + x2 = -18.761663039 + 19 x2 = -18.761663039 + 19 Combine like terms: -18.761663039 + 19 = 0.238336961 x2 = 0.238336961 Simplifying x2 = 0.238336961 Take the square root of each side: x = {-0.488197666, 0.488197666}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.145051915, 6.145051915, -0.488197666, 0.488197666}Solution
x = {-6.145051915, 6.145051915, -0.488197666, 0.488197666}
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