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Simplifying 4x4 + 7x2 + -10 = 0 Reorder the terms: -10 + 7x2 + 4x4 = 0 Solving -10 + 7x2 + 4x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.5 + 1.75x2 + x4 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 1.75x2 + 2.5 + x4 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 1.75x2 + x4 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 1.75x2 + x4 = 0 + 2.5 1.75x2 + x4 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 1.75x2 + x4 = 2.5 The x term is 1.75x2. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x2 + 0.765625 + x4 = 2.5 + 0.765625 Reorder the terms: 0.765625 + 1.75x2 + x4 = 2.5 + 0.765625 Combine like terms: 2.5 + 0.765625 = 3.265625 0.765625 + 1.75x2 + x4 = 3.265625 Factor a perfect square on the left side: (x2 + 0.875)(x2 + 0.875) = 3.265625 Calculate the square root of the right side: 1.807104037 Break this problem into two subproblems by setting (x2 + 0.875) equal to 1.807104037 and -1.807104037.Subproblem 1
x2 + 0.875 = 1.807104037 Simplifying x2 + 0.875 = 1.807104037 Reorder the terms: 0.875 + x2 = 1.807104037 Solving 0.875 + x2 = 1.807104037 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x2 = 1.807104037 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x2 = 1.807104037 + -0.875 x2 = 1.807104037 + -0.875 Combine like terms: 1.807104037 + -0.875 = 0.932104037 x2 = 0.932104037 Simplifying x2 = 0.932104037 Take the square root of each side: x = {-0.965455352, 0.965455352}Subproblem 2
x2 + 0.875 = -1.807104037 Simplifying x2 + 0.875 = -1.807104037 Reorder the terms: 0.875 + x2 = -1.807104037 Solving 0.875 + x2 = -1.807104037 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x2 = -1.807104037 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x2 = -1.807104037 + -0.875 x2 = -1.807104037 + -0.875 Combine like terms: -1.807104037 + -0.875 = -2.682104037 x2 = -2.682104037 Simplifying x2 = -2.682104037 Reorder the terms: 2.682104037 + x2 = -2.682104037 + 2.682104037 Combine like terms: -2.682104037 + 2.682104037 = 0.000000000 2.682104037 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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