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Simplifying 14x4 + -11x2 + -36 = 0 Reorder the terms: -36 + -11x2 + 14x4 = 0 Solving -36 + -11x2 + 14x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -2.571428571 + -0.7857142857x2 + x4 = 0 Move the constant term to the right: Add '2.571428571' to each side of the equation. -2.571428571 + -0.7857142857x2 + 2.571428571 + x4 = 0 + 2.571428571 Reorder the terms: -2.571428571 + 2.571428571 + -0.7857142857x2 + x4 = 0 + 2.571428571 Combine like terms: -2.571428571 + 2.571428571 = 0.000000000 0.000000000 + -0.7857142857x2 + x4 = 0 + 2.571428571 -0.7857142857x2 + x4 = 0 + 2.571428571 Combine like terms: 0 + 2.571428571 = 2.571428571 -0.7857142857x2 + x4 = 2.571428571 The x term is -0.7857142857x2. Take half its coefficient (-0.3928571429). Square it (0.1543367347) and add it to both sides. Add '0.1543367347' to each side of the equation. -0.7857142857x2 + 0.1543367347 + x4 = 2.571428571 + 0.1543367347 Reorder the terms: 0.1543367347 + -0.7857142857x2 + x4 = 2.571428571 + 0.1543367347 Combine like terms: 2.571428571 + 0.1543367347 = 2.7257653057 0.1543367347 + -0.7857142857x2 + x4 = 2.7257653057 Factor a perfect square on the left side: (x2 + -0.3928571429)(x2 + -0.3928571429) = 2.7257653057 Calculate the square root of the right side: 1.65098919 Break this problem into two subproblems by setting (x2 + -0.3928571429) equal to 1.65098919 and -1.65098919.Subproblem 1
x2 + -0.3928571429 = 1.65098919 Simplifying x2 + -0.3928571429 = 1.65098919 Reorder the terms: -0.3928571429 + x2 = 1.65098919 Solving -0.3928571429 + x2 = 1.65098919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3928571429' to each side of the equation. -0.3928571429 + 0.3928571429 + x2 = 1.65098919 + 0.3928571429 Combine like terms: -0.3928571429 + 0.3928571429 = 0.0000000000 0.0000000000 + x2 = 1.65098919 + 0.3928571429 x2 = 1.65098919 + 0.3928571429 Combine like terms: 1.65098919 + 0.3928571429 = 2.0438463329 x2 = 2.0438463329 Simplifying x2 = 2.0438463329 Take the square root of each side: x = {-1.429631537, 1.429631537}Subproblem 2
x2 + -0.3928571429 = -1.65098919 Simplifying x2 + -0.3928571429 = -1.65098919 Reorder the terms: -0.3928571429 + x2 = -1.65098919 Solving -0.3928571429 + x2 = -1.65098919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3928571429' to each side of the equation. -0.3928571429 + 0.3928571429 + x2 = -1.65098919 + 0.3928571429 Combine like terms: -0.3928571429 + 0.3928571429 = 0.0000000000 0.0000000000 + x2 = -1.65098919 + 0.3928571429 x2 = -1.65098919 + 0.3928571429 Combine like terms: -1.65098919 + 0.3928571429 = -1.2581320471 x2 = -1.2581320471 Simplifying x2 = -1.2581320471 Reorder the terms: 1.2581320471 + x2 = -1.2581320471 + 1.2581320471 Combine like terms: -1.2581320471 + 1.2581320471 = 0.0000000000 1.2581320471 + x2 = 0.0000000000 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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