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Simplifying 0.000000000735x4 + -0.2538x2 + 1.6768 = 0 Reorder the terms: 1.6768 + -0.2538x2 + 0.000000000735x4 = 0 Solving 1.6768 + -0.2538x2 + 0.000000000735x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.000000000735 the coefficient of the squared term: Divide each side by '0.000000000735'. 2281360544 + -345306122.4x2 + x4 = 0 Move the constant term to the right: Add '-2281360544' to each side of the equation. 2281360544 + -345306122.4x2 + -2281360544 + x4 = 0 + -2281360544 Reorder the terms: 2281360544 + -2281360544 + -345306122.4x2 + x4 = 0 + -2281360544 Combine like terms: 2281360544 + -2281360544 = 0 0 + -345306122.4x2 + x4 = 0 + -2281360544 -345306122.4x2 + x4 = 0 + -2281360544 Combine like terms: 0 + -2281360544 = -2281360544 -345306122.4x2 + x4 = -2281360544 The x term is -345306122.4x2. Take half its coefficient (-172653061.2). Square it (29809079540000000) and add it to both sides. Add '29809079540000000' to each side of the equation. -345306122.4x2 + 29809079540000000 + x4 = -2281360544 + 29809079540000000 Reorder the terms: 29809079540000000 + -345306122.4x2 + x4 = -2281360544 + 29809079540000000 Combine like terms: -2281360544 + 29809079540000000 = 29809077258639456 29809079540000000 + -345306122.4x2 + x4 = 29809077258639456 Factor a perfect square on the left side: (x2 + -172653061.2)(x2 + -172653061.2) = 29809077258639456 Calculate the square root of the right side: 172653054.588210098 Break this problem into two subproblems by setting (x2 + -172653061.2) equal to 172653054.588210098 and -172653054.588210098.Subproblem 1
x2 + -172653061.2 = 172653054.588210098 Simplifying x2 + -172653061.2 = 172653054.588210098 Reorder the terms: -172653061.2 + x2 = 172653054.588210098 Solving -172653061.2 + x2 = 172653054.588210098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '172653061.2' to each side of the equation. -172653061.2 + 172653061.2 + x2 = 172653054.588210098 + 172653061.2 Combine like terms: -172653061.2 + 172653061.2 = 0.0 0.0 + x2 = 172653054.588210098 + 172653061.2 x2 = 172653054.588210098 + 172653061.2 Combine like terms: 172653054.588210098 + 172653061.2 = 345306115.788210098 x2 = 345306115.788210098 Simplifying x2 = 345306115.788210098 Take the square root of each side: x = {-18582.414153931, 18582.414153931}Subproblem 2
x2 + -172653061.2 = -172653054.588210098 Simplifying x2 + -172653061.2 = -172653054.588210098 Reorder the terms: -172653061.2 + x2 = -172653054.588210098 Solving -172653061.2 + x2 = -172653054.588210098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '172653061.2' to each side of the equation. -172653061.2 + 172653061.2 + x2 = -172653054.588210098 + 172653061.2 Combine like terms: -172653061.2 + 172653061.2 = 0.0 0.0 + x2 = -172653054.588210098 + 172653061.2 x2 = -172653054.588210098 + 172653061.2 Combine like terms: -172653054.588210098 + 172653061.2 = 6.611789902 x2 = 6.611789902 Simplifying x2 = 6.611789902 Take the square root of each side: x = {-2.571340098, 2.571340098}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-18582.414153931, 18582.414153931, -2.571340098, 2.571340098}
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