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Simplifying (9X2 + -7X + 12) + (7X2 + 9X + -44) = 0 Reorder the terms: (12 + -7X + 9X2) + (7X2 + 9X + -44) = 0 Remove parenthesis around (12 + -7X + 9X2) 12 + -7X + 9X2 + (7X2 + 9X + -44) = 0 Reorder the terms: 12 + -7X + 9X2 + (-44 + 9X + 7X2) = 0 Remove parenthesis around (-44 + 9X + 7X2) 12 + -7X + 9X2 + -44 + 9X + 7X2 = 0 Reorder the terms: 12 + -44 + -7X + 9X + 9X2 + 7X2 = 0 Combine like terms: 12 + -44 = -32 -32 + -7X + 9X + 9X2 + 7X2 = 0 Combine like terms: -7X + 9X = 2X -32 + 2X + 9X2 + 7X2 = 0 Combine like terms: 9X2 + 7X2 = 16X2 -32 + 2X + 16X2 = 0 Solving -32 + 2X + 16X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + X + 8X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-16 + X + 8X2)' equal to zero and attempt to solve: Simplifying -16 + X + 8X2 = 0 Solving -16 + X + 8X2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2 + 0.125X + X2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.125X + 2 + X2 = 0 + 2 Reorder the terms: -2 + 2 + 0.125X + X2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.125X + X2 = 0 + 2 0.125X + X2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.125X + X2 = 2 The X term is X. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.125X + 0.25 + X2 = 2 + 0.25 Reorder the terms: 0.25 + 0.125X + X2 = 2 + 0.25 Combine like terms: 2 + 0.25 = 2.25 0.25 + 0.125X + X2 = 2.25 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 2.25 Calculate the square root of the right side: 1.5 Break this problem into two subproblems by setting (X + 0.5) equal to 1.5 and -1.5.Subproblem 1
X + 0.5 = 1.5 Simplifying X + 0.5 = 1.5 Reorder the terms: 0.5 + X = 1.5 Solving 0.5 + X = 1.5 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = 1.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 1.5 + -0.5 X = 1.5 + -0.5 Combine like terms: 1.5 + -0.5 = 1 X = 1 Simplifying X = 1Subproblem 2
X + 0.5 = -1.5 Simplifying X + 0.5 = -1.5 Reorder the terms: 0.5 + X = -1.5 Solving 0.5 + X = -1.5 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = -1.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -1.5 + -0.5 X = -1.5 + -0.5 Combine like terms: -1.5 + -0.5 = -2 X = -2 Simplifying X = -2Solution
The solution to the problem is based on the solutions from the subproblems. X = {1, -2}Solution
X = {1, -2}
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