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Simplifying (-3x4 + 7x2 + 1) + -1(x4 + 6x2 + -9) = 0 Reorder the terms: (1 + 7x2 + -3x4) + -1(x4 + 6x2 + -9) = 0 Remove parenthesis around (1 + 7x2 + -3x4) 1 + 7x2 + -3x4 + -1(x4 + 6x2 + -9) = 0 Reorder the terms: 1 + 7x2 + -3x4 + -1(-9 + 6x2 + x4) = 0 1 + 7x2 + -3x4 + (-9 * -1 + 6x2 * -1 + x4 * -1) = 0 1 + 7x2 + -3x4 + (9 + -6x2 + -1x4) = 0 Reorder the terms: 1 + 9 + 7x2 + -6x2 + -3x4 + -1x4 = 0 Combine like terms: 1 + 9 = 10 10 + 7x2 + -6x2 + -3x4 + -1x4 = 0 Combine like terms: 7x2 + -6x2 = 1x2 10 + 1x2 + -3x4 + -1x4 = 0 Combine like terms: -3x4 + -1x4 = -4x4 10 + 1x2 + -4x4 = 0 Solving 10 + 1x2 + -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 + -0.25x2 + x4 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -0.25x2 + 2.5 + x4 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -0.25x2 + x4 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -0.25x2 + x4 = 0 + 2.5 -0.25x2 + x4 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -0.25x2 + x4 = 2.5 The x term is -0.25x2. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x2 + 0.015625 + x4 = 2.5 + 0.015625 Reorder the terms: 0.015625 + -0.25x2 + x4 = 2.5 + 0.015625 Combine like terms: 2.5 + 0.015625 = 2.515625 0.015625 + -0.25x2 + x4 = 2.515625 Factor a perfect square on the left side: (x2 + -0.125)(x2 + -0.125) = 2.515625 Calculate the square root of the right side: 1.586072193 Break this problem into two subproblems by setting (x2 + -0.125) equal to 1.586072193 and -1.586072193.Subproblem 1
x2 + -0.125 = 1.586072193 Simplifying x2 + -0.125 = 1.586072193 Reorder the terms: -0.125 + x2 = 1.586072193 Solving -0.125 + x2 = 1.586072193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x2 = 1.586072193 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x2 = 1.586072193 + 0.125 x2 = 1.586072193 + 0.125 Combine like terms: 1.586072193 + 0.125 = 1.711072193 x2 = 1.711072193 Simplifying x2 = 1.711072193 Take the square root of each side: x = {-1.308079582, 1.308079582}Subproblem 2
x2 + -0.125 = -1.586072193 Simplifying x2 + -0.125 = -1.586072193 Reorder the terms: -0.125 + x2 = -1.586072193 Solving -0.125 + x2 = -1.586072193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x2 = -1.586072193 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x2 = -1.586072193 + 0.125 x2 = -1.586072193 + 0.125 Combine like terms: -1.586072193 + 0.125 = -1.461072193 x2 = -1.461072193 Simplifying x2 = -1.461072193 Reorder the terms: 1.461072193 + x2 = -1.461072193 + 1.461072193 Combine like terms: -1.461072193 + 1.461072193 = 0.000000000 1.461072193 + 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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