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Simplifying 8 = X2 + -9X + -7 Reorder the terms: 8 = -7 + -9X + X2 Solving 8 = -7 + -9X + X2 Solving for variable 'X'. Combine like terms: 8 + 7 = 15 15 + 9X + -1X2 = -7 + -9X + X2 + 7 + 9X + -1X2 Reorder the terms: 15 + 9X + -1X2 = -7 + 7 + -9X + 9X + X2 + -1X2 Combine like terms: -7 + 7 = 0 15 + 9X + -1X2 = 0 + -9X + 9X + X2 + -1X2 15 + 9X + -1X2 = -9X + 9X + X2 + -1X2 Combine like terms: -9X + 9X = 0 15 + 9X + -1X2 = 0 + X2 + -1X2 15 + 9X + -1X2 = X2 + -1X2 Combine like terms: X2 + -1X2 = 0 15 + 9X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -15 + -9X + X2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -9X + 15 + X2 = 0 + 15 Reorder the terms: -15 + 15 + -9X + X2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -9X + X2 = 0 + 15 -9X + X2 = 0 + 15 Combine like terms: 0 + 15 = 15 -9X + X2 = 15 The X term is -9X. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9X + 20.25 + X2 = 15 + 20.25 Reorder the terms: 20.25 + -9X + X2 = 15 + 20.25 Combine like terms: 15 + 20.25 = 35.25 20.25 + -9X + X2 = 35.25 Factor a perfect square on the left side: (X + -4.5)(X + -4.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (X + -4.5) equal to 5.937171044 and -5.937171044.Subproblem 1
X + -4.5 = 5.937171044 Simplifying X + -4.5 = 5.937171044 Reorder the terms: -4.5 + X = 5.937171044 Solving -4.5 + X = 5.937171044 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + X = 5.937171044 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + X = 5.937171044 + 4.5 X = 5.937171044 + 4.5 Combine like terms: 5.937171044 + 4.5 = 10.437171044 X = 10.437171044 Simplifying X = 10.437171044Subproblem 2
X + -4.5 = -5.937171044 Simplifying X + -4.5 = -5.937171044 Reorder the terms: -4.5 + X = -5.937171044 Solving -4.5 + X = -5.937171044 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + X = -5.937171044 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + X = -5.937171044 + 4.5 X = -5.937171044 + 4.5 Combine like terms: -5.937171044 + 4.5 = -1.437171044 X = -1.437171044 Simplifying X = -1.437171044Solution
The solution to the problem is based on the solutions from the subproblems. X = {10.437171044, -1.437171044}
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