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Simplifying 0 = -5X2 + 8X + 9 Reorder the terms: 0 = 9 + 8X + -5X2 Solving 0 = 9 + 8X + -5X2 Solving for variable 'X'. Combine like terms: 0 + -9 = -9 -9 + -8X + 5X2 = 9 + 8X + -5X2 + -9 + -8X + 5X2 Reorder the terms: -9 + -8X + 5X2 = 9 + -9 + 8X + -8X + -5X2 + 5X2 Combine like terms: 9 + -9 = 0 -9 + -8X + 5X2 = 0 + 8X + -8X + -5X2 + 5X2 -9 + -8X + 5X2 = 8X + -8X + -5X2 + 5X2 Combine like terms: 8X + -8X = 0 -9 + -8X + 5X2 = 0 + -5X2 + 5X2 -9 + -8X + 5X2 = -5X2 + 5X2 Combine like terms: -5X2 + 5X2 = 0 -9 + -8X + 5X2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.8 + -1.6X + X2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + -1.6X + 1.8 + X2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + -1.6X + X2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + -1.6X + X2 = 0 + 1.8 -1.6X + X2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 -1.6X + X2 = 1.8 The X term is -1.6X. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6X + 0.64 + X2 = 1.8 + 0.64 Reorder the terms: 0.64 + -1.6X + X2 = 1.8 + 0.64 Combine like terms: 1.8 + 0.64 = 2.44 0.64 + -1.6X + X2 = 2.44 Factor a perfect square on the left side: (X + -0.8)(X + -0.8) = 2.44 Calculate the square root of the right side: 1.562049935 Break this problem into two subproblems by setting (X + -0.8) equal to 1.562049935 and -1.562049935.Subproblem 1
X + -0.8 = 1.562049935 Simplifying X + -0.8 = 1.562049935 Reorder the terms: -0.8 + X = 1.562049935 Solving -0.8 + X = 1.562049935 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + X = 1.562049935 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + X = 1.562049935 + 0.8 X = 1.562049935 + 0.8 Combine like terms: 1.562049935 + 0.8 = 2.362049935 X = 2.362049935 Simplifying X = 2.362049935Subproblem 2
X + -0.8 = -1.562049935 Simplifying X + -0.8 = -1.562049935 Reorder the terms: -0.8 + X = -1.562049935 Solving -0.8 + X = -1.562049935 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + X = -1.562049935 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + X = -1.562049935 + 0.8 X = -1.562049935 + 0.8 Combine like terms: -1.562049935 + 0.8 = -0.762049935 X = -0.762049935 Simplifying X = -0.762049935Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.362049935, -0.762049935}
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