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Simplifying x4 + -14x2 + 45 = 9 Reorder the terms: 45 + -14x2 + x4 = 9 Solving 45 + -14x2 + x4 = 9 Solving for variable 'x'. Reorder the terms: 45 + -9 + -14x2 + x4 = 9 + -9 Combine like terms: 45 + -9 = 36 36 + -14x2 + x4 = 9 + -9 Combine like terms: 9 + -9 = 0 36 + -14x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -14x2 + -36 + x4 = 0 + -36 Reorder the terms: 36 + -36 + -14x2 + x4 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -14x2 + x4 = 0 + -36 -14x2 + x4 = 0 + -36 Combine like terms: 0 + -36 = -36 -14x2 + x4 = -36 The x term is -14x2. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x2 + 49 + x4 = -36 + 49 Reorder the terms: 49 + -14x2 + x4 = -36 + 49 Combine like terms: -36 + 49 = 13 49 + -14x2 + x4 = 13 Factor a perfect square on the left side: (x2 + -7)(x2 + -7) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x2 + -7) equal to 3.605551275 and -3.605551275.Subproblem 1
x2 + -7 = 3.605551275 Simplifying x2 + -7 = 3.605551275 Reorder the terms: -7 + x2 = 3.605551275 Solving -7 + x2 = 3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x2 = 3.605551275 + 7 Combine like terms: -7 + 7 = 0 0 + x2 = 3.605551275 + 7 x2 = 3.605551275 + 7 Combine like terms: 3.605551275 + 7 = 10.605551275 x2 = 10.605551275 Simplifying x2 = 10.605551275 Take the square root of each side: x = {-3.256616538, 3.256616538}Subproblem 2
x2 + -7 = -3.605551275 Simplifying x2 + -7 = -3.605551275 Reorder the terms: -7 + x2 = -3.605551275 Solving -7 + x2 = -3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x2 = -3.605551275 + 7 Combine like terms: -7 + 7 = 0 0 + x2 = -3.605551275 + 7 x2 = -3.605551275 + 7 Combine like terms: -3.605551275 + 7 = 3.394448725 x2 = 3.394448725 Simplifying x2 = 3.394448725 Take the square root of each side: x = {-1.842402976, 1.842402976}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.256616538, 3.256616538, -1.842402976, 1.842402976}
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