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Simplifying 0 = -5X2 + 6X + 3 Reorder the terms: 0 = 3 + 6X + -5X2 Solving 0 = 3 + 6X + -5X2 Solving for variable 'X'. Combine like terms: 0 + -3 = -3 -3 + -6X + 5X2 = 3 + 6X + -5X2 + -3 + -6X + 5X2 Reorder the terms: -3 + -6X + 5X2 = 3 + -3 + 6X + -6X + -5X2 + 5X2 Combine like terms: 3 + -3 = 0 -3 + -6X + 5X2 = 0 + 6X + -6X + -5X2 + 5X2 -3 + -6X + 5X2 = 6X + -6X + -5X2 + 5X2 Combine like terms: 6X + -6X = 0 -3 + -6X + 5X2 = 0 + -5X2 + 5X2 -3 + -6X + 5X2 = -5X2 + 5X2 Combine like terms: -5X2 + 5X2 = 0 -3 + -6X + 5X2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + -1.2X + X2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -1.2X + 0.6 + X2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -1.2X + X2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -1.2X + X2 = 0 + 0.6 -1.2X + X2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -1.2X + X2 = 0.6 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 = 0.6 + 0.36 Reorder the terms: 0.36 + -1.2X + X2 = 0.6 + 0.36 Combine like terms: 0.6 + 0.36 = 0.96 0.36 + -1.2X + X2 = 0.96 Factor a perfect square on the left side: (X + -0.6)(X + -0.6) = 0.96 Calculate the square root of the right side: 0.979795897 Break this problem into two subproblems by setting (X + -0.6) equal to 0.979795897 and -0.979795897.Subproblem 1
X + -0.6 = 0.979795897 Simplifying X + -0.6 = 0.979795897 Reorder the terms: -0.6 + X = 0.979795897 Solving -0.6 + X = 0.979795897 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 = 0.979795897 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + X = 0.979795897 + 0.6 X = 0.979795897 + 0.6 Combine like terms: 0.979795897 + 0.6 = 1.579795897 X = 1.579795897 Simplifying X = 1.579795897Subproblem 2
X + -0.6 = -0.979795897 Simplifying X + -0.6 = -0.979795897 Reorder the terms: -0.6 + X = -0.979795897 Solving -0.6 + X = -0.979795897 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 = -0.979795897 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + X = -0.979795897 + 0.6 X = -0.979795897 + 0.6 Combine like terms: -0.979795897 + 0.6 = -0.379795897 X = -0.379795897 Simplifying X = -0.379795897Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.579795897, -0.379795897}
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