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Simplifying 15X4 + -1(30X2) + 7 = 0 Remove parenthesis around (30X2) 15X4 + -1 * 30X2 + 7 = 0 Multiply -1 * 30 15X4 + -30X2 + 7 = 0 Reorder the terms: 7 + -30X2 + 15X4 = 0 Solving 7 + -30X2 + 15X4 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 0.4666666667 + -2X2 + X4 = 0 Move the constant term to the right: Add '-0.4666666667' to each side of the equation. 0.4666666667 + -2X2 + -0.4666666667 + X4 = 0 + -0.4666666667 Reorder the terms: 0.4666666667 + -0.4666666667 + -2X2 + X4 = 0 + -0.4666666667 Combine like terms: 0.4666666667 + -0.4666666667 = 0.0000000000 0.0000000000 + -2X2 + X4 = 0 + -0.4666666667 -2X2 + X4 = 0 + -0.4666666667 Combine like terms: 0 + -0.4666666667 = -0.4666666667 -2X2 + X4 = -0.4666666667 The X term is -2X2. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2X2 + 1 + X4 = -0.4666666667 + 1 Reorder the terms: 1 + -2X2 + X4 = -0.4666666667 + 1 Combine like terms: -0.4666666667 + 1 = 0.5333333333 1 + -2X2 + X4 = 0.5333333333 Factor a perfect square on the left side: (X2 + -1)(X2 + -1) = 0.5333333333 Calculate the square root of the right side: 0.730296743 Break this problem into two subproblems by setting (X2 + -1) equal to 0.730296743 and -0.730296743.Subproblem 1
X2 + -1 = 0.730296743 Simplifying X2 + -1 = 0.730296743 Reorder the terms: -1 + X2 = 0.730296743 Solving -1 + X2 = 0.730296743 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + X2 = 0.730296743 + 1 Combine like terms: -1 + 1 = 0 0 + X2 = 0.730296743 + 1 X2 = 0.730296743 + 1 Combine like terms: 0.730296743 + 1 = 1.730296743 X2 = 1.730296743 Simplifying X2 = 1.730296743 Take the square root of each side: X = {-1.315407444, 1.315407444}Subproblem 2
X2 + -1 = -0.730296743 Simplifying X2 + -1 = -0.730296743 Reorder the terms: -1 + X2 = -0.730296743 Solving -1 + X2 = -0.730296743 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + X2 = -0.730296743 + 1 Combine like terms: -1 + 1 = 0 0 + X2 = -0.730296743 + 1 X2 = -0.730296743 + 1 Combine like terms: -0.730296743 + 1 = 0.269703257 X2 = 0.269703257 Simplifying X2 = 0.269703257 Take the square root of each side: X = {-0.519329623, 0.519329623}Solution
The solution to the problem is based on the solutions from the subproblems. X = {-1.315407444, 1.315407444, -0.519329623, 0.519329623}
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