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Simplifying 5x4 + -49x2 = 72 Reorder the terms: -49x2 + 5x4 = 72 Solving -49x2 + 5x4 = 72 Solving for variable 'x'. Reorder the terms: -72 + -49x2 + 5x4 = 72 + -72 Combine like terms: 72 + -72 = 0 -72 + -49x2 + 5x4 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -14.4 + -9.8x2 + x4 = 0 Move the constant term to the right: Add '14.4' to each side of the equation. -14.4 + -9.8x2 + 14.4 + x4 = 0 + 14.4 Reorder the terms: -14.4 + 14.4 + -9.8x2 + x4 = 0 + 14.4 Combine like terms: -14.4 + 14.4 = 0.0 0.0 + -9.8x2 + x4 = 0 + 14.4 -9.8x2 + x4 = 0 + 14.4 Combine like terms: 0 + 14.4 = 14.4 -9.8x2 + x4 = 14.4 The x term is -9.8x2. Take half its coefficient (-4.9). Square it (24.01) and add it to both sides. Add '24.01' to each side of the equation. -9.8x2 + 24.01 + x4 = 14.4 + 24.01 Reorder the terms: 24.01 + -9.8x2 + x4 = 14.4 + 24.01 Combine like terms: 14.4 + 24.01 = 38.41 24.01 + -9.8x2 + x4 = 38.41 Factor a perfect square on the left side: (x2 + -4.9)(x2 + -4.9) = 38.41 Calculate the square root of the right side: 6.197580173 Break this problem into two subproblems by setting (x2 + -4.9) equal to 6.197580173 and -6.197580173.Subproblem 1
x2 + -4.9 = 6.197580173 Simplifying x2 + -4.9 = 6.197580173 Reorder the terms: -4.9 + x2 = 6.197580173 Solving -4.9 + x2 = 6.197580173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.9' to each side of the equation. -4.9 + 4.9 + x2 = 6.197580173 + 4.9 Combine like terms: -4.9 + 4.9 = 0.0 0.0 + x2 = 6.197580173 + 4.9 x2 = 6.197580173 + 4.9 Combine like terms: 6.197580173 + 4.9 = 11.097580173 x2 = 11.097580173 Simplifying x2 = 11.097580173 Take the square root of each side: x = {-3.331303074, 3.331303074}Subproblem 2
x2 + -4.9 = -6.197580173 Simplifying x2 + -4.9 = -6.197580173 Reorder the terms: -4.9 + x2 = -6.197580173 Solving -4.9 + x2 = -6.197580173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.9' to each side of the equation. -4.9 + 4.9 + x2 = -6.197580173 + 4.9 Combine like terms: -4.9 + 4.9 = 0.0 0.0 + x2 = -6.197580173 + 4.9 x2 = -6.197580173 + 4.9 Combine like terms: -6.197580173 + 4.9 = -1.297580173 x2 = -1.297580173 Simplifying x2 = -1.297580173 Reorder the terms: 1.297580173 + x2 = -1.297580173 + 1.297580173 Combine like terms: -1.297580173 + 1.297580173 = 0.000000000 1.297580173 + 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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