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Simplifying 2.4x4 + -36.4x2 = -9.2 Reorder the terms: -36.4x2 + 2.4x4 = -9.2 Solving -36.4x2 + 2.4x4 = -9.2 Solving for variable 'x'. Reorder the terms: 9.2 + -36.4x2 + 2.4x4 = -9.2 + 9.2 Combine like terms: -9.2 + 9.2 = 0.0 9.2 + -36.4x2 + 2.4x4 = 0.0 Begin completing the square. Divide all terms by 2.4 the coefficient of the squared term: Divide each side by '2.4'. 3.833333333 + -15.16666667x2 + x4 = 0 Move the constant term to the right: Add '-3.833333333' to each side of the equation. 3.833333333 + -15.16666667x2 + -3.833333333 + x4 = 0 + -3.833333333 Reorder the terms: 3.833333333 + -3.833333333 + -15.16666667x2 + x4 = 0 + -3.833333333 Combine like terms: 3.833333333 + -3.833333333 = 0.000000000 0.000000000 + -15.16666667x2 + x4 = 0 + -3.833333333 -15.16666667x2 + x4 = 0 + -3.833333333 Combine like terms: 0 + -3.833333333 = -3.833333333 -15.16666667x2 + x4 = -3.833333333 The x term is -15.16666667x2. Take half its coefficient (-7.583333335). Square it (57.50694447) and add it to both sides. Add '57.50694447' to each side of the equation. -15.16666667x2 + 57.50694447 + x4 = -3.833333333 + 57.50694447 Reorder the terms: 57.50694447 + -15.16666667x2 + x4 = -3.833333333 + 57.50694447 Combine like terms: -3.833333333 + 57.50694447 = 53.673611137 57.50694447 + -15.16666667x2 + x4 = 53.673611137 Factor a perfect square on the left side: (x2 + -7.583333335)(x2 + -7.583333335) = 53.673611137 Calculate the square root of the right side: 7.32622762 Break this problem into two subproblems by setting (x2 + -7.583333335) equal to 7.32622762 and -7.32622762.Subproblem 1
x2 + -7.583333335 = 7.32622762 Simplifying x2 + -7.583333335 = 7.32622762 Reorder the terms: -7.583333335 + x2 = 7.32622762 Solving -7.583333335 + x2 = 7.32622762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.583333335' to each side of the equation. -7.583333335 + 7.583333335 + x2 = 7.32622762 + 7.583333335 Combine like terms: -7.583333335 + 7.583333335 = 0.000000000 0.000000000 + x2 = 7.32622762 + 7.583333335 x2 = 7.32622762 + 7.583333335 Combine like terms: 7.32622762 + 7.583333335 = 14.909560955 x2 = 14.909560955 Simplifying x2 = 14.909560955 Take the square root of each side: x = {-3.861290064, 3.861290064}Subproblem 2
x2 + -7.583333335 = -7.32622762 Simplifying x2 + -7.583333335 = -7.32622762 Reorder the terms: -7.583333335 + x2 = -7.32622762 Solving -7.583333335 + x2 = -7.32622762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.583333335' to each side of the equation. -7.583333335 + 7.583333335 + x2 = -7.32622762 + 7.583333335 Combine like terms: -7.583333335 + 7.583333335 = 0.000000000 0.000000000 + x2 = -7.32622762 + 7.583333335 x2 = -7.32622762 + 7.583333335 Combine like terms: -7.32622762 + 7.583333335 = 0.257105715 x2 = 0.257105715 Simplifying x2 = 0.257105715 Take the square root of each side: x = {-0.507055929, 0.507055929}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.861290064, 3.861290064, -0.507055929, 0.507055929}
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