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Simplifying 4X2 = 5 + -9X Solving 4X2 = 5 + -9X Solving for variable 'X'. Reorder the terms: -5 + 9X + 4X2 = 5 + -9X + -5 + 9X Reorder the terms: -5 + 9X + 4X2 = 5 + -5 + -9X + 9X Combine like terms: 5 + -5 = 0 -5 + 9X + 4X2 = 0 + -9X + 9X -5 + 9X + 4X2 = -9X + 9X Combine like terms: -9X + 9X = 0 -5 + 9X + 4X2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + 2.25X + X2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 2.25X + 1.25 + X2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 2.25X + X2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 2.25X + X2 = 0 + 1.25 2.25X + X2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 2.25X + X2 = 1.25 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 = 1.25 + 1.265625 Reorder the terms: 1.265625 + 2.25X + X2 = 1.25 + 1.265625 Combine like terms: 1.25 + 1.265625 = 2.515625 1.265625 + 2.25X + X2 = 2.515625 Factor a perfect square on the left side: (X + 1.125)(X + 1.125) = 2.515625 Calculate the square root of the right side: 1.586072193 Break this problem into two subproblems by setting (X + 1.125) equal to 1.586072193 and -1.586072193.Subproblem 1
X + 1.125 = 1.586072193 Simplifying X + 1.125 = 1.586072193 Reorder the terms: 1.125 + X = 1.586072193 Solving 1.125 + X = 1.586072193 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 = 1.586072193 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + X = 1.586072193 + -1.125 X = 1.586072193 + -1.125 Combine like terms: 1.586072193 + -1.125 = 0.461072193 X = 0.461072193 Simplifying X = 0.461072193Subproblem 2
X + 1.125 = -1.586072193 Simplifying X + 1.125 = -1.586072193 Reorder the terms: 1.125 + X = -1.586072193 Solving 1.125 + X = -1.586072193 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 = -1.586072193 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + X = -1.586072193 + -1.125 X = -1.586072193 + -1.125 Combine like terms: -1.586072193 + -1.125 = -2.711072193 X = -2.711072193 Simplifying X = -2.711072193Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.461072193, -2.711072193}
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