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Simplifying 7 = -2X2 + -18X + 5 Reorder the terms: 7 = 5 + -18X + -2X2 Solving 7 = 5 + -18X + -2X2 Solving for variable 'X'. Combine like terms: 7 + -5 = 2 2 + 18X + 2X2 = 5 + -18X + -2X2 + -5 + 18X + 2X2 Reorder the terms: 2 + 18X + 2X2 = 5 + -5 + -18X + 18X + -2X2 + 2X2 Combine like terms: 5 + -5 = 0 2 + 18X + 2X2 = 0 + -18X + 18X + -2X2 + 2X2 2 + 18X + 2X2 = -18X + 18X + -2X2 + 2X2 Combine like terms: -18X + 18X = 0 2 + 18X + 2X2 = 0 + -2X2 + 2X2 2 + 18X + 2X2 = -2X2 + 2X2 Combine like terms: -2X2 + 2X2 = 0 2 + 18X + 2X2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 9X + X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 9X + X2)' equal to zero and attempt to solve: Simplifying 1 + 9X + X2 = 0 Solving 1 + 9X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 9X + -1 + X2 = 0 + -1 Reorder the terms: 1 + -1 + 9X + X2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 9X + X2 = 0 + -1 9X + X2 = 0 + -1 Combine like terms: 0 + -1 = -1 9X + X2 = -1 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 = -1 + 20.25 Reorder the terms: 20.25 + 9X + X2 = -1 + 20.25 Combine like terms: -1 + 20.25 = 19.25 20.25 + 9X + X2 = 19.25 Factor a perfect square on the left side: (X + 4.5)(X + 4.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (X + 4.5) equal to 4.387482194 and -4.387482194.Subproblem 1
X + 4.5 = 4.387482194 Simplifying X + 4.5 = 4.387482194 Reorder the terms: 4.5 + X = 4.387482194 Solving 4.5 + X = 4.387482194 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 = 4.387482194 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + X = 4.387482194 + -4.5 X = 4.387482194 + -4.5 Combine like terms: 4.387482194 + -4.5 = -0.112517806 X = -0.112517806 Simplifying X = -0.112517806Subproblem 2
X + 4.5 = -4.387482194 Simplifying X + 4.5 = -4.387482194 Reorder the terms: 4.5 + X = -4.387482194 Solving 4.5 + X = -4.387482194 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 = -4.387482194 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + X = -4.387482194 + -4.5 X = -4.387482194 + -4.5 Combine like terms: -4.387482194 + -4.5 = -8.887482194 X = -8.887482194 Simplifying X = -8.887482194Solution
The solution to the problem is based on the solutions from the subproblems. X = {-0.112517806, -8.887482194}Solution
X = {-0.112517806, -8.887482194}
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