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Simplifying 5X2 + -6X + -1 = 0 Reorder the terms: -1 + -6X + 5X2 = 0 Solving -1 + -6X + 5X2 = 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 + -1.2X + X2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -1.2X + 0.2 + X2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -1.2X + X2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -1.2X + X2 = 0 + 0.2 -1.2X + X2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -1.2X + X2 = 0.2 The X term is -1.2X. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2X + 0.36 + X2 = 0.2 + 0.36 Reorder the terms: 0.36 + -1.2X + X2 = 0.2 + 0.36 Combine like terms: 0.2 + 0.36 = 0.56 0.36 + -1.2X + X2 = 0.56 Factor a perfect square on the left side: (X + -0.6)(X + -0.6) = 0.56 Calculate the square root of the right side: 0.748331477 Break this problem into two subproblems by setting (X + -0.6) equal to 0.748331477 and -0.748331477.Subproblem 1
X + -0.6 = 0.748331477 Simplifying X + -0.6 = 0.748331477 Reorder the terms: -0.6 + X = 0.748331477 Solving -0.6 + X = 0.748331477 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + X = 0.748331477 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + X = 0.748331477 + 0.6 X = 0.748331477 + 0.6 Combine like terms: 0.748331477 + 0.6 = 1.348331477 X = 1.348331477 Simplifying X = 1.348331477Subproblem 2
X + -0.6 = -0.748331477 Simplifying X + -0.6 = -0.748331477 Reorder the terms: -0.6 + X = -0.748331477 Solving -0.6 + X = -0.748331477 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + X = -0.748331477 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + X = -0.748331477 + 0.6 X = -0.748331477 + 0.6 Combine like terms: -0.748331477 + 0.6 = -0.148331477 X = -0.148331477 Simplifying X = -0.148331477Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.348331477, -0.148331477}
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