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Simplifying 5X2 + 9X + -16 = 0 Reorder the terms: -16 + 9X + 5X2 = 0 Solving -16 + 9X + 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'. -3.2 + 1.8X + X2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + 1.8X + 3.2 + X2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + 1.8X + X2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + 1.8X + X2 = 0 + 3.2 1.8X + X2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 1.8X + X2 = 3.2 The X term is 1.8X. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8X + 0.81 + X2 = 3.2 + 0.81 Reorder the terms: 0.81 + 1.8X + X2 = 3.2 + 0.81 Combine like terms: 3.2 + 0.81 = 4.01 0.81 + 1.8X + X2 = 4.01 Factor a perfect square on the left side: (X + 0.9)(X + 0.9) = 4.01 Calculate the square root of the right side: 2.002498439 Break this problem into two subproblems by setting (X + 0.9) equal to 2.002498439 and -2.002498439.Subproblem 1
X + 0.9 = 2.002498439 Simplifying X + 0.9 = 2.002498439 Reorder the terms: 0.9 + X = 2.002498439 Solving 0.9 + X = 2.002498439 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + X = 2.002498439 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + X = 2.002498439 + -0.9 X = 2.002498439 + -0.9 Combine like terms: 2.002498439 + -0.9 = 1.102498439 X = 1.102498439 Simplifying X = 1.102498439Subproblem 2
X + 0.9 = -2.002498439 Simplifying X + 0.9 = -2.002498439 Reorder the terms: 0.9 + X = -2.002498439 Solving 0.9 + X = -2.002498439 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + X = -2.002498439 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + X = -2.002498439 + -0.9 X = -2.002498439 + -0.9 Combine like terms: -2.002498439 + -0.9 = -2.902498439 X = -2.902498439 Simplifying X = -2.902498439Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.102498439, -2.902498439}
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