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Simplifying 9x4 = 30x2 + 25 Reorder the terms: 9x4 = 25 + 30x2 Solving 9x4 = 25 + 30x2 Solving for variable 'x'. Reorder the terms: -25 + -30x2 + 9x4 = 25 + 30x2 + -25 + -30x2 Reorder the terms: -25 + -30x2 + 9x4 = 25 + -25 + 30x2 + -30x2 Combine like terms: 25 + -25 = 0 -25 + -30x2 + 9x4 = 0 + 30x2 + -30x2 -25 + -30x2 + 9x4 = 30x2 + -30x2 Combine like terms: 30x2 + -30x2 = 0 -25 + -30x2 + 9x4 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.777777778 + -3.333333333x2 + x4 = 0 Move the constant term to the right: Add '2.777777778' to each side of the equation. -2.777777778 + -3.333333333x2 + 2.777777778 + x4 = 0 + 2.777777778 Reorder the terms: -2.777777778 + 2.777777778 + -3.333333333x2 + x4 = 0 + 2.777777778 Combine like terms: -2.777777778 + 2.777777778 = 0.000000000 0.000000000 + -3.333333333x2 + x4 = 0 + 2.777777778 -3.333333333x2 + x4 = 0 + 2.777777778 Combine like terms: 0 + 2.777777778 = 2.777777778 -3.333333333x2 + x4 = 2.777777778 The x term is -3.333333333x2. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333x2 + 2.777777779 + x4 = 2.777777778 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x2 + x4 = 2.777777778 + 2.777777779 Combine like terms: 2.777777778 + 2.777777779 = 5.555555557 2.777777779 + -3.333333333x2 + x4 = 5.555555557 Factor a perfect square on the left side: (x2 + -1.666666667)(x2 + -1.666666667) = 5.555555557 Calculate the square root of the right side: 2.357022604 Break this problem into two subproblems by setting (x2 + -1.666666667) equal to 2.357022604 and -2.357022604.Subproblem 1
x2 + -1.666666667 = 2.357022604 Simplifying x2 + -1.666666667 = 2.357022604 Reorder the terms: -1.666666667 + x2 = 2.357022604 Solving -1.666666667 + x2 = 2.357022604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x2 = 2.357022604 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x2 = 2.357022604 + 1.666666667 x2 = 2.357022604 + 1.666666667 Combine like terms: 2.357022604 + 1.666666667 = 4.023689271 x2 = 4.023689271 Simplifying x2 = 4.023689271 Take the square root of each side: x = {-2.005913575, 2.005913575}Subproblem 2
x2 + -1.666666667 = -2.357022604 Simplifying x2 + -1.666666667 = -2.357022604 Reorder the terms: -1.666666667 + x2 = -2.357022604 Solving -1.666666667 + x2 = -2.357022604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x2 = -2.357022604 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x2 = -2.357022604 + 1.666666667 x2 = -2.357022604 + 1.666666667 Combine like terms: -2.357022604 + 1.666666667 = -0.690355937 x2 = -0.690355937 Simplifying x2 = -0.690355937 Reorder the terms: 0.690355937 + x2 = -0.690355937 + 0.690355937 Combine like terms: -0.690355937 + 0.690355937 = 0.000000000 0.690355937 + 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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