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Simplifying 5x4 + -20x2 + 10.8 = 0 Reorder the terms: 10.8 + -20x2 + 5x4 = 0 Solving 10.8 + -20x2 + 5x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.16 + -4x2 + x4 = 0 Move the constant term to the right: Add '-2.16' to each side of the equation. 2.16 + -4x2 + -2.16 + x4 = 0 + -2.16 Reorder the terms: 2.16 + -2.16 + -4x2 + x4 = 0 + -2.16 Combine like terms: 2.16 + -2.16 = 0.00 0.00 + -4x2 + x4 = 0 + -2.16 -4x2 + x4 = 0 + -2.16 Combine like terms: 0 + -2.16 = -2.16 -4x2 + x4 = -2.16 The x term is -4x2. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x2 + 4 + x4 = -2.16 + 4 Reorder the terms: 4 + -4x2 + x4 = -2.16 + 4 Combine like terms: -2.16 + 4 = 1.84 4 + -4x2 + x4 = 1.84 Factor a perfect square on the left side: (x2 + -2)(x2 + -2) = 1.84 Calculate the square root of the right side: 1.356465997 Break this problem into two subproblems by setting (x2 + -2) equal to 1.356465997 and -1.356465997.Subproblem 1
x2 + -2 = 1.356465997 Simplifying x2 + -2 = 1.356465997 Reorder the terms: -2 + x2 = 1.356465997 Solving -2 + x2 = 1.356465997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x2 = 1.356465997 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = 1.356465997 + 2 x2 = 1.356465997 + 2 Combine like terms: 1.356465997 + 2 = 3.356465997 x2 = 3.356465997 Simplifying x2 = 3.356465997 Take the square root of each side: x = {-1.832066046, 1.832066046}Subproblem 2
x2 + -2 = -1.356465997 Simplifying x2 + -2 = -1.356465997 Reorder the terms: -2 + x2 = -1.356465997 Solving -2 + x2 = -1.356465997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x2 = -1.356465997 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = -1.356465997 + 2 x2 = -1.356465997 + 2 Combine like terms: -1.356465997 + 2 = 0.643534003 x2 = 0.643534003 Simplifying x2 = 0.643534003 Take the square root of each side: x = {-0.802205711, 0.802205711}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.832066046, 1.832066046, -0.802205711, 0.802205711}
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