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Simplifying 4x4 + -8x2 + -3 = 0 Reorder the terms: -3 + -8x2 + 4x4 = 0 Solving -3 + -8x2 + 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'. -0.75 + -2x2 + x4 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -2x2 + 0.75 + x4 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -2x2 + x4 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -2x2 + x4 = 0 + 0.75 -2x2 + x4 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -2x2 + x4 = 0.75 The x term is -2x2. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x2 + 1 + x4 = 0.75 + 1 Reorder the terms: 1 + -2x2 + x4 = 0.75 + 1 Combine like terms: 0.75 + 1 = 1.75 1 + -2x2 + x4 = 1.75 Factor a perfect square on the left side: (x2 + -1)(x2 + -1) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (x2 + -1) equal to 1.322875656 and -1.322875656.Subproblem 1
x2 + -1 = 1.322875656 Simplifying x2 + -1 = 1.322875656 Reorder the terms: -1 + x2 = 1.322875656 Solving -1 + x2 = 1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x2 = 1.322875656 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = 1.322875656 + 1 x2 = 1.322875656 + 1 Combine like terms: 1.322875656 + 1 = 2.322875656 x2 = 2.322875656 Simplifying x2 = 2.322875656 Take the square root of each side: x = {-1.524098309, 1.524098309}Subproblem 2
x2 + -1 = -1.322875656 Simplifying x2 + -1 = -1.322875656 Reorder the terms: -1 + x2 = -1.322875656 Solving -1 + x2 = -1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x2 = -1.322875656 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = -1.322875656 + 1 x2 = -1.322875656 + 1 Combine like terms: -1.322875656 + 1 = -0.322875656 x2 = -0.322875656 Simplifying x2 = -0.322875656 Reorder the terms: 0.322875656 + x2 = -0.322875656 + 0.322875656 Combine like terms: -0.322875656 + 0.322875656 = 0.000000000 0.322875656 + 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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