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Simplifying (3X2 + 9X + -1) + (-5X2 + 6X + -10) = 0 Reorder the terms: (-1 + 9X + 3X2) + (-5X2 + 6X + -10) = 0 Remove parenthesis around (-1 + 9X + 3X2) -1 + 9X + 3X2 + (-5X2 + 6X + -10) = 0 Reorder the terms: -1 + 9X + 3X2 + (-10 + 6X + -5X2) = 0 Remove parenthesis around (-10 + 6X + -5X2) -1 + 9X + 3X2 + -10 + 6X + -5X2 = 0 Reorder the terms: -1 + -10 + 9X + 6X + 3X2 + -5X2 = 0 Combine like terms: -1 + -10 = -11 -11 + 9X + 6X + 3X2 + -5X2 = 0 Combine like terms: 9X + 6X = 15X -11 + 15X + 3X2 + -5X2 = 0 Combine like terms: 3X2 + -5X2 = -2X2 -11 + 15X + -2X2 = 0 Solving -11 + 15X + -2X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 5.5 + -7.5X + X2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + -7.5X + -5.5 + X2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + -7.5X + X2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + -7.5X + X2 = 0 + -5.5 -7.5X + X2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 -7.5X + X2 = -5.5 The X term is -7.5X. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5X + 14.0625 + X2 = -5.5 + 14.0625 Reorder the terms: 14.0625 + -7.5X + X2 = -5.5 + 14.0625 Combine like terms: -5.5 + 14.0625 = 8.5625 14.0625 + -7.5X + X2 = 8.5625 Factor a perfect square on the left side: (X + -3.75)(X + -3.75) = 8.5625 Calculate the square root of the right side: 2.926174978 Break this problem into two subproblems by setting (X + -3.75) equal to 2.926174978 and -2.926174978.Subproblem 1
X + -3.75 = 2.926174978 Simplifying X + -3.75 = 2.926174978 Reorder the terms: -3.75 + X = 2.926174978 Solving -3.75 + X = 2.926174978 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + X = 2.926174978 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + X = 2.926174978 + 3.75 X = 2.926174978 + 3.75 Combine like terms: 2.926174978 + 3.75 = 6.676174978 X = 6.676174978 Simplifying X = 6.676174978Subproblem 2
X + -3.75 = -2.926174978 Simplifying X + -3.75 = -2.926174978 Reorder the terms: -3.75 + X = -2.926174978 Solving -3.75 + X = -2.926174978 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + X = -2.926174978 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + X = -2.926174978 + 3.75 X = -2.926174978 + 3.75 Combine like terms: -2.926174978 + 3.75 = 0.823825022 X = 0.823825022 Simplifying X = 0.823825022Solution
The solution to the problem is based on the solutions from the subproblems. X = {6.676174978, 0.823825022}
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