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Simplifying 2x4 + -15x2 + 9 = 0 Reorder the terms: 9 + -15x2 + 2x4 = 0 Solving 9 + -15x2 + 2x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + -7.5x2 + x4 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -7.5x2 + -4.5 + x4 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -7.5x2 + x4 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -7.5x2 + x4 = 0 + -4.5 -7.5x2 + x4 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -7.5x2 + x4 = -4.5 The x term is -7.5x2. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x2 + 14.0625 + x4 = -4.5 + 14.0625 Reorder the terms: 14.0625 + -7.5x2 + x4 = -4.5 + 14.0625 Combine like terms: -4.5 + 14.0625 = 9.5625 14.0625 + -7.5x2 + x4 = 9.5625 Factor a perfect square on the left side: (x2 + -3.75)(x2 + -3.75) = 9.5625 Calculate the square root of the right side: 3.092329219 Break this problem into two subproblems by setting (x2 + -3.75) equal to 3.092329219 and -3.092329219.Subproblem 1
x2 + -3.75 = 3.092329219 Simplifying x2 + -3.75 = 3.092329219 Reorder the terms: -3.75 + x2 = 3.092329219 Solving -3.75 + x2 = 3.092329219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x2 = 3.092329219 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x2 = 3.092329219 + 3.75 x2 = 3.092329219 + 3.75 Combine like terms: 3.092329219 + 3.75 = 6.842329219 x2 = 6.842329219 Simplifying x2 = 6.842329219 Take the square root of each side: x = {-2.615784628, 2.615784628}Subproblem 2
x2 + -3.75 = -3.092329219 Simplifying x2 + -3.75 = -3.092329219 Reorder the terms: -3.75 + x2 = -3.092329219 Solving -3.75 + x2 = -3.092329219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x2 = -3.092329219 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x2 = -3.092329219 + 3.75 x2 = -3.092329219 + 3.75 Combine like terms: -3.092329219 + 3.75 = 0.657670781 x2 = 0.657670781 Simplifying x2 = 0.657670781 Take the square root of each side: x = {-0.810969038, 0.810969038}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.615784628, 2.615784628, -0.810969038, 0.810969038}
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