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Simplifying x4 + -15x2 = -12 Reorder the terms: -15x2 + x4 = -12 Solving -15x2 + x4 = -12 Solving for variable 'x'. Reorder the terms: 12 + -15x2 + x4 = -12 + 12 Combine like terms: -12 + 12 = 0 12 + -15x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -15x2 + -12 + x4 = 0 + -12 Reorder the terms: 12 + -12 + -15x2 + x4 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -15x2 + x4 = 0 + -12 -15x2 + x4 = 0 + -12 Combine like terms: 0 + -12 = -12 -15x2 + x4 = -12 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 = -12 + 56.25 Reorder the terms: 56.25 + -15x2 + x4 = -12 + 56.25 Combine like terms: -12 + 56.25 = 44.25 56.25 + -15x2 + x4 = 44.25 Factor a perfect square on the left side: (x2 + -7.5)(x2 + -7.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (x2 + -7.5) equal to 6.652067348 and -6.652067348.Subproblem 1
x2 + -7.5 = 6.652067348 Simplifying x2 + -7.5 = 6.652067348 Reorder the terms: -7.5 + x2 = 6.652067348 Solving -7.5 + x2 = 6.652067348 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 = 6.652067348 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x2 = 6.652067348 + 7.5 x2 = 6.652067348 + 7.5 Combine like terms: 6.652067348 + 7.5 = 14.152067348 x2 = 14.152067348 Simplifying x2 = 14.152067348 Take the square root of each side: x = {-3.761923358, 3.761923358}Subproblem 2
x2 + -7.5 = -6.652067348 Simplifying x2 + -7.5 = -6.652067348 Reorder the terms: -7.5 + x2 = -6.652067348 Solving -7.5 + x2 = -6.652067348 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 = -6.652067348 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x2 = -6.652067348 + 7.5 x2 = -6.652067348 + 7.5 Combine like terms: -6.652067348 + 7.5 = 0.847932652 x2 = 0.847932652 Simplifying x2 = 0.847932652 Take the square root of each side: x = {-0.920832586, 0.920832586}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.761923358, 3.761923358, -0.920832586, 0.920832586}
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