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Simplifying x4 + -15x2 + 4 = 0 Reorder the terms: 4 + -15x2 + x4 = 0 Solving 4 + -15x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -15x2 + -4 + x4 = 0 + -4 Reorder the terms: 4 + -4 + -15x2 + x4 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -15x2 + x4 = 0 + -4 -15x2 + x4 = 0 + -4 Combine like terms: 0 + -4 = -4 -15x2 + x4 = -4 The x term is -15x2. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x2 + 56.25 + x4 = -4 + 56.25 Reorder the terms: 56.25 + -15x2 + x4 = -4 + 56.25 Combine like terms: -4 + 56.25 = 52.25 56.25 + -15x2 + x4 = 52.25 Factor a perfect square on the left side: (x2 + -7.5)(x2 + -7.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (x2 + -7.5) equal to 7.228416147 and -7.228416147.Subproblem 1
x2 + -7.5 = 7.228416147 Simplifying x2 + -7.5 = 7.228416147 Reorder the terms: -7.5 + x2 = 7.228416147 Solving -7.5 + x2 = 7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x2 = 7.228416147 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x2 = 7.228416147 + 7.5 x2 = 7.228416147 + 7.5 Combine like terms: 7.228416147 + 7.5 = 14.728416147 x2 = 14.728416147 Simplifying x2 = 14.728416147 Take the square root of each side: x = {-3.837761867, 3.837761867}Subproblem 2
x2 + -7.5 = -7.228416147 Simplifying x2 + -7.5 = -7.228416147 Reorder the terms: -7.5 + x2 = -7.228416147 Solving -7.5 + x2 = -7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x2 = -7.228416147 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x2 = -7.228416147 + 7.5 x2 = -7.228416147 + 7.5 Combine like terms: -7.228416147 + 7.5 = 0.271583853 x2 = 0.271583853 Simplifying x2 = 0.271583853 Take the square root of each side: x = {-0.521137077, 0.521137077}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.837761867, 3.837761867, -0.521137077, 0.521137077}
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