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Simplifying 7x4 + -13x2 + -15 = 0 Reorder the terms: -15 + -13x2 + 7x4 = 0 Solving -15 + -13x2 + 7x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.142857143 + -1.857142857x2 + x4 = 0 Move the constant term to the right: Add '2.142857143' to each side of the equation. -2.142857143 + -1.857142857x2 + 2.142857143 + x4 = 0 + 2.142857143 Reorder the terms: -2.142857143 + 2.142857143 + -1.857142857x2 + x4 = 0 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + -1.857142857x2 + x4 = 0 + 2.142857143 -1.857142857x2 + x4 = 0 + 2.142857143 Combine like terms: 0 + 2.142857143 = 2.142857143 -1.857142857x2 + x4 = 2.142857143 The x term is -1.857142857x2. Take half its coefficient (-0.9285714285). Square it (0.8622448978) and add it to both sides. Add '0.8622448978' to each side of the equation. -1.857142857x2 + 0.8622448978 + x4 = 2.142857143 + 0.8622448978 Reorder the terms: 0.8622448978 + -1.857142857x2 + x4 = 2.142857143 + 0.8622448978 Combine like terms: 2.142857143 + 0.8622448978 = 3.0051020408 0.8622448978 + -1.857142857x2 + x4 = 3.0051020408 Factor a perfect square on the left side: (x2 + -0.9285714285)(x2 + -0.9285714285) = 3.0051020408 Calculate the square root of the right side: 1.733523014 Break this problem into two subproblems by setting (x2 + -0.9285714285) equal to 1.733523014 and -1.733523014.Subproblem 1
x2 + -0.9285714285 = 1.733523014 Simplifying x2 + -0.9285714285 = 1.733523014 Reorder the terms: -0.9285714285 + x2 = 1.733523014 Solving -0.9285714285 + x2 = 1.733523014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9285714285' to each side of the equation. -0.9285714285 + 0.9285714285 + x2 = 1.733523014 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + x2 = 1.733523014 + 0.9285714285 x2 = 1.733523014 + 0.9285714285 Combine like terms: 1.733523014 + 0.9285714285 = 2.6620944425 x2 = 2.6620944425 Simplifying x2 = 2.6620944425 Take the square root of each side: x = {-1.631592609, 1.631592609}Subproblem 2
x2 + -0.9285714285 = -1.733523014 Simplifying x2 + -0.9285714285 = -1.733523014 Reorder the terms: -0.9285714285 + x2 = -1.733523014 Solving -0.9285714285 + x2 = -1.733523014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9285714285' to each side of the equation. -0.9285714285 + 0.9285714285 + x2 = -1.733523014 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + x2 = -1.733523014 + 0.9285714285 x2 = -1.733523014 + 0.9285714285 Combine like terms: -1.733523014 + 0.9285714285 = -0.8049515855 x2 = -0.8049515855 Simplifying x2 = -0.8049515855 Reorder the terms: 0.8049515855 + x2 = -0.8049515855 + 0.8049515855 Combine like terms: -0.8049515855 + 0.8049515855 = 0.0000000000 0.8049515855 + 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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