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Simplifying 4X2 = 8 + -9X Solving 4X2 = 8 + -9X Solving for variable 'X'. Reorder the terms: -8 + 9X + 4X2 = 8 + -9X + -8 + 9X Reorder the terms: -8 + 9X + 4X2 = 8 + -8 + -9X + 9X Combine like terms: 8 + -8 = 0 -8 + 9X + 4X2 = 0 + -9X + 9X -8 + 9X + 4X2 = -9X + 9X Combine like terms: -9X + 9X = 0 -8 + 9X + 4X2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2 + 2.25X + X2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 2.25X + 2 + X2 = 0 + 2 Reorder the terms: -2 + 2 + 2.25X + X2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 2.25X + X2 = 0 + 2 2.25X + X2 = 0 + 2 Combine like terms: 0 + 2 = 2 2.25X + X2 = 2 The X term is 2.25X. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25X + 1.265625 + X2 = 2 + 1.265625 Reorder the terms: 1.265625 + 2.25X + X2 = 2 + 1.265625 Combine like terms: 2 + 1.265625 = 3.265625 1.265625 + 2.25X + X2 = 3.265625 Factor a perfect square on the left side: (X + 1.125)(X + 1.125) = 3.265625 Calculate the square root of the right side: 1.807104037 Break this problem into two subproblems by setting (X + 1.125) equal to 1.807104037 and -1.807104037.Subproblem 1
X + 1.125 = 1.807104037 Simplifying X + 1.125 = 1.807104037 Reorder the terms: 1.125 + X = 1.807104037 Solving 1.125 + X = 1.807104037 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + X = 1.807104037 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + X = 1.807104037 + -1.125 X = 1.807104037 + -1.125 Combine like terms: 1.807104037 + -1.125 = 0.682104037 X = 0.682104037 Simplifying X = 0.682104037Subproblem 2
X + 1.125 = -1.807104037 Simplifying X + 1.125 = -1.807104037 Reorder the terms: 1.125 + X = -1.807104037 Solving 1.125 + X = -1.807104037 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + X = -1.807104037 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + X = -1.807104037 + -1.125 X = -1.807104037 + -1.125 Combine like terms: -1.807104037 + -1.125 = -2.932104037 X = -2.932104037 Simplifying X = -2.932104037Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.682104037, -2.932104037}
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