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Simplifying x4 = 34x2 + -25 Reorder the terms: x4 = -25 + 34x2 Solving x4 = -25 + 34x2 Solving for variable 'x'. Reorder the terms: 25 + -34x2 + x4 = -25 + 34x2 + 25 + -34x2 Reorder the terms: 25 + -34x2 + x4 = -25 + 25 + 34x2 + -34x2 Combine like terms: -25 + 25 = 0 25 + -34x2 + x4 = 0 + 34x2 + -34x2 25 + -34x2 + x4 = 34x2 + -34x2 Combine like terms: 34x2 + -34x2 = 0 25 + -34x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -34x2 + -25 + x4 = 0 + -25 Reorder the terms: 25 + -25 + -34x2 + x4 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -34x2 + x4 = 0 + -25 -34x2 + x4 = 0 + -25 Combine like terms: 0 + -25 = -25 -34x2 + x4 = -25 The x term is -34x2. Take half its coefficient (-17). Square it (289) and add it to both sides. Add '289' to each side of the equation. -34x2 + 289 + x4 = -25 + 289 Reorder the terms: 289 + -34x2 + x4 = -25 + 289 Combine like terms: -25 + 289 = 264 289 + -34x2 + x4 = 264 Factor a perfect square on the left side: (x2 + -17)(x2 + -17) = 264 Calculate the square root of the right side: 16.248076809 Break this problem into two subproblems by setting (x2 + -17) equal to 16.248076809 and -16.248076809.Subproblem 1
x2 + -17 = 16.248076809 Simplifying x2 + -17 = 16.248076809 Reorder the terms: -17 + x2 = 16.248076809 Solving -17 + x2 = 16.248076809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x2 = 16.248076809 + 17 Combine like terms: -17 + 17 = 0 0 + x2 = 16.248076809 + 17 x2 = 16.248076809 + 17 Combine like terms: 16.248076809 + 17 = 33.248076809 x2 = 33.248076809 Simplifying x2 = 33.248076809 Take the square root of each side: x = {-5.766114533, 5.766114533}Subproblem 2
x2 + -17 = -16.248076809 Simplifying x2 + -17 = -16.248076809 Reorder the terms: -17 + x2 = -16.248076809 Solving -17 + x2 = -16.248076809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x2 = -16.248076809 + 17 Combine like terms: -17 + 17 = 0 0 + x2 = -16.248076809 + 17 x2 = -16.248076809 + 17 Combine like terms: -16.248076809 + 17 = 0.751923191 x2 = 0.751923191 Simplifying x2 = 0.751923191 Take the square root of each side: x = {-0.867135048, 0.867135048}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.766114533, 5.766114533, -0.867135048, 0.867135048}
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