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Simplifying 26X4 + -25X2 + 4 = 0 Reorder the terms: 4 + -25X2 + 26X4 = 0 Solving 4 + -25X2 + 26X4 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 26 the coefficient of the squared term: Divide each side by '26'. 0.1538461538 + -0.9615384615X2 + X4 = 0 Move the constant term to the right: Add '-0.1538461538' to each side of the equation. 0.1538461538 + -0.9615384615X2 + -0.1538461538 + X4 = 0 + -0.1538461538 Reorder the terms: 0.1538461538 + -0.1538461538 + -0.9615384615X2 + X4 = 0 + -0.1538461538 Combine like terms: 0.1538461538 + -0.1538461538 = 0.0000000000 0.0000000000 + -0.9615384615X2 + X4 = 0 + -0.1538461538 -0.9615384615X2 + X4 = 0 + -0.1538461538 Combine like terms: 0 + -0.1538461538 = -0.1538461538 -0.9615384615X2 + X4 = -0.1538461538 The X term is -0.9615384615X2. Take half its coefficient (-0.4807692308). Square it (0.2311390533) and add it to both sides. Add '0.2311390533' to each side of the equation. -0.9615384615X2 + 0.2311390533 + X4 = -0.1538461538 + 0.2311390533 Reorder the terms: 0.2311390533 + -0.9615384615X2 + X4 = -0.1538461538 + 0.2311390533 Combine like terms: -0.1538461538 + 0.2311390533 = 0.0772928995 0.2311390533 + -0.9615384615X2 + X4 = 0.0772928995 Factor a perfect square on the left side: (X2 + -0.4807692308)(X2 + -0.4807692308) = 0.0772928995 Calculate the square root of the right side: 0.278016006 Break this problem into two subproblems by setting (X2 + -0.4807692308) equal to 0.278016006 and -0.278016006.Subproblem 1
X2 + -0.4807692308 = 0.278016006 Simplifying X2 + -0.4807692308 = 0.278016006 Reorder the terms: -0.4807692308 + X2 = 0.278016006 Solving -0.4807692308 + X2 = 0.278016006 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.4807692308' to each side of the equation. -0.4807692308 + 0.4807692308 + X2 = 0.278016006 + 0.4807692308 Combine like terms: -0.4807692308 + 0.4807692308 = 0.0000000000 0.0000000000 + X2 = 0.278016006 + 0.4807692308 X2 = 0.278016006 + 0.4807692308 Combine like terms: 0.278016006 + 0.4807692308 = 0.7587852368 X2 = 0.7587852368 Simplifying X2 = 0.7587852368 Take the square root of each side: X = {-0.871082796, 0.871082796}Subproblem 2
X2 + -0.4807692308 = -0.278016006 Simplifying X2 + -0.4807692308 = -0.278016006 Reorder the terms: -0.4807692308 + X2 = -0.278016006 Solving -0.4807692308 + X2 = -0.278016006 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.4807692308' to each side of the equation. -0.4807692308 + 0.4807692308 + X2 = -0.278016006 + 0.4807692308 Combine like terms: -0.4807692308 + 0.4807692308 = 0.0000000000 0.0000000000 + X2 = -0.278016006 + 0.4807692308 X2 = -0.278016006 + 0.4807692308 Combine like terms: -0.278016006 + 0.4807692308 = 0.2027532248 X2 = 0.2027532248 Simplifying X2 = 0.2027532248 Take the square root of each side: X = {-0.450281273, 0.450281273}Solution
The solution to the problem is based on the solutions from the subproblems. X = {-0.871082796, 0.871082796, -0.450281273, 0.450281273}
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