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Simplifying (2x4 + 5x2 + -7x + -4) + (-7x4 + -3x2 + 7x + 5) = 0 Reorder the terms: (-4 + -7x + 5x2 + 2x4) + (-7x4 + -3x2 + 7x + 5) = 0 Remove parenthesis around (-4 + -7x + 5x2 + 2x4) -4 + -7x + 5x2 + 2x4 + (-7x4 + -3x2 + 7x + 5) = 0 Reorder the terms: -4 + -7x + 5x2 + 2x4 + (5 + 7x + -3x2 + -7x4) = 0 Remove parenthesis around (5 + 7x + -3x2 + -7x4) -4 + -7x + 5x2 + 2x4 + 5 + 7x + -3x2 + -7x4 = 0 Reorder the terms: -4 + 5 + -7x + 7x + 5x2 + -3x2 + 2x4 + -7x4 = 0 Combine like terms: -4 + 5 = 1 1 + -7x + 7x + 5x2 + -3x2 + 2x4 + -7x4 = 0 Combine like terms: -7x + 7x = 0 1 + 0 + 5x2 + -3x2 + 2x4 + -7x4 = 0 1 + 5x2 + -3x2 + 2x4 + -7x4 = 0 Combine like terms: 5x2 + -3x2 = 2x2 1 + 2x2 + 2x4 + -7x4 = 0 Combine like terms: 2x4 + -7x4 = -5x4 1 + 2x2 + -5x4 = 0 Solving 1 + 2x2 + -5x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.2 + -0.4x2 + x4 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -0.4x2 + 0.2 + x4 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -0.4x2 + x4 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -0.4x2 + x4 = 0 + 0.2 -0.4x2 + x4 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -0.4x2 + x4 = 0.2 The x term is -0.4x2. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x2 + 0.04 + x4 = 0.2 + 0.04 Reorder the terms: 0.04 + -0.4x2 + x4 = 0.2 + 0.04 Combine like terms: 0.2 + 0.04 = 0.24 0.04 + -0.4x2 + x4 = 0.24 Factor a perfect square on the left side: (x2 + -0.2)(x2 + -0.2) = 0.24 Calculate the square root of the right side: 0.489897949 Break this problem into two subproblems by setting (x2 + -0.2) equal to 0.489897949 and -0.489897949.Subproblem 1
x2 + -0.2 = 0.489897949 Simplifying x2 + -0.2 = 0.489897949 Reorder the terms: -0.2 + x2 = 0.489897949 Solving -0.2 + x2 = 0.489897949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x2 = 0.489897949 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x2 = 0.489897949 + 0.2 x2 = 0.489897949 + 0.2 Combine like terms: 0.489897949 + 0.2 = 0.689897949 x2 = 0.689897949 Simplifying x2 = 0.689897949 Take the square root of each side: x = {-0.830600957, 0.830600957}Subproblem 2
x2 + -0.2 = -0.489897949 Simplifying x2 + -0.2 = -0.489897949 Reorder the terms: -0.2 + x2 = -0.489897949 Solving -0.2 + x2 = -0.489897949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x2 = -0.489897949 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x2 = -0.489897949 + 0.2 x2 = -0.489897949 + 0.2 Combine like terms: -0.489897949 + 0.2 = -0.289897949 x2 = -0.289897949 Simplifying x2 = -0.289897949 Reorder the terms: 0.289897949 + x2 = -0.289897949 + 0.289897949 Combine like terms: -0.289897949 + 0.289897949 = 0.000000000 0.289897949 + 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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