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Simplifying x2(x2 + -1) = 17x2 + -25 Reorder the terms: x2(-1 + x2) = 17x2 + -25 (-1 * x2 + x2 * x2) = 17x2 + -25 (-1x2 + x4) = 17x2 + -25 Reorder the terms: -1x2 + x4 = -25 + 17x2 Solving -1x2 + x4 = -25 + 17x2 Solving for variable 'x'. Reorder the terms: 25 + -1x2 + -17x2 + x4 = -25 + 17x2 + 25 + -17x2 Combine like terms: -1x2 + -17x2 = -18x2 25 + -18x2 + x4 = -25 + 17x2 + 25 + -17x2 Reorder the terms: 25 + -18x2 + x4 = -25 + 25 + 17x2 + -17x2 Combine like terms: -25 + 25 = 0 25 + -18x2 + x4 = 0 + 17x2 + -17x2 25 + -18x2 + x4 = 17x2 + -17x2 Combine like terms: 17x2 + -17x2 = 0 25 + -18x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -18x2 + -25 + x4 = 0 + -25 Reorder the terms: 25 + -25 + -18x2 + x4 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -18x2 + x4 = 0 + -25 -18x2 + x4 = 0 + -25 Combine like terms: 0 + -25 = -25 -18x2 + x4 = -25 The x term is -18x2. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x2 + 81 + x4 = -25 + 81 Reorder the terms: 81 + -18x2 + x4 = -25 + 81 Combine like terms: -25 + 81 = 56 81 + -18x2 + x4 = 56 Factor a perfect square on the left side: (x2 + -9)(x2 + -9) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (x2 + -9) equal to 7.483314774 and -7.483314774.Subproblem 1
x2 + -9 = 7.483314774 Simplifying x2 + -9 = 7.483314774 Reorder the terms: -9 + x2 = 7.483314774 Solving -9 + x2 = 7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x2 = 7.483314774 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = 7.483314774 + 9 x2 = 7.483314774 + 9 Combine like terms: 7.483314774 + 9 = 16.483314774 x2 = 16.483314774 Simplifying x2 = 16.483314774 Take the square root of each side: x = {-4.059964873, 4.059964873}Subproblem 2
x2 + -9 = -7.483314774 Simplifying x2 + -9 = -7.483314774 Reorder the terms: -9 + x2 = -7.483314774 Solving -9 + x2 = -7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x2 = -7.483314774 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = -7.483314774 + 9 x2 = -7.483314774 + 9 Combine like terms: -7.483314774 + 9 = 1.516685226 x2 = 1.516685226 Simplifying x2 = 1.516685226 Take the square root of each side: x = {-1.231537749, 1.231537749}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.059964873, 4.059964873, -1.231537749, 1.231537749}
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