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Simplifying 6x4 + -14x2 = 9 Reorder the terms: -14x2 + 6x4 = 9 Solving -14x2 + 6x4 = 9 Solving for variable 'x'. Reorder the terms: -9 + -14x2 + 6x4 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -14x2 + 6x4 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.5 + -2.333333333x2 + x4 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -2.333333333x2 + 1.5 + x4 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -2.333333333x2 + x4 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -2.333333333x2 + x4 = 0 + 1.5 -2.333333333x2 + x4 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -2.333333333x2 + x4 = 1.5 The x term is -2.333333333x2. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333x2 + 1.361111112 + x4 = 1.5 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x2 + x4 = 1.5 + 1.361111112 Combine like terms: 1.5 + 1.361111112 = 2.861111112 1.361111112 + -2.333333333x2 + x4 = 2.861111112 Factor a perfect square on the left side: (x2 + -1.166666667)(x2 + -1.166666667) = 2.861111112 Calculate the square root of the right side: 1.691481928 Break this problem into two subproblems by setting (x2 + -1.166666667) equal to 1.691481928 and -1.691481928.Subproblem 1
x2 + -1.166666667 = 1.691481928 Simplifying x2 + -1.166666667 = 1.691481928 Reorder the terms: -1.166666667 + x2 = 1.691481928 Solving -1.166666667 + x2 = 1.691481928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x2 = 1.691481928 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x2 = 1.691481928 + 1.166666667 x2 = 1.691481928 + 1.166666667 Combine like terms: 1.691481928 + 1.166666667 = 2.858148595 x2 = 2.858148595 Simplifying x2 = 2.858148595 Take the square root of each side: x = {-1.690605985, 1.690605985}Subproblem 2
x2 + -1.166666667 = -1.691481928 Simplifying x2 + -1.166666667 = -1.691481928 Reorder the terms: -1.166666667 + x2 = -1.691481928 Solving -1.166666667 + x2 = -1.691481928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x2 = -1.691481928 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x2 = -1.691481928 + 1.166666667 x2 = -1.691481928 + 1.166666667 Combine like terms: -1.691481928 + 1.166666667 = -0.524815261 x2 = -0.524815261 Simplifying x2 = -0.524815261 Reorder the terms: 0.524815261 + x2 = -0.524815261 + 0.524815261 Combine like terms: -0.524815261 + 0.524815261 = 0.000000000 0.524815261 + 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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