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Simplifying -16x2 + 18x + 5 = 0 Reorder the terms: 5 + 18x + -16x2 = 0 Solving 5 + 18x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.3125 + -1.125x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -1.125x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -1.125x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -1.125x + x2 = 0 + 0.3125 -1.125x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -1.125x + x2 = 0.3125 The x term is -1.125x. Take half its coefficient (-0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. -1.125x + 0.31640625 + x2 = 0.3125 + 0.31640625 Reorder the terms: 0.31640625 + -1.125x + x2 = 0.3125 + 0.31640625 Combine like terms: 0.3125 + 0.31640625 = 0.62890625 0.31640625 + -1.125x + x2 = 0.62890625 Factor a perfect square on the left side: (x + -0.5625)(x + -0.5625) = 0.62890625 Calculate the square root of the right side: 0.793036096 Break this problem into two subproblems by setting (x + -0.5625) equal to 0.793036096 and -0.793036096.Subproblem 1
x + -0.5625 = 0.793036096 Simplifying x + -0.5625 = 0.793036096 Reorder the terms: -0.5625 + x = 0.793036096 Solving -0.5625 + x = 0.793036096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = 0.793036096 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = 0.793036096 + 0.5625 x = 0.793036096 + 0.5625 Combine like terms: 0.793036096 + 0.5625 = 1.355536096 x = 1.355536096 Simplifying x = 1.355536096Subproblem 2
x + -0.5625 = -0.793036096 Simplifying x + -0.5625 = -0.793036096 Reorder the terms: -0.5625 + x = -0.793036096 Solving -0.5625 + x = -0.793036096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = -0.793036096 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = -0.793036096 + 0.5625 x = -0.793036096 + 0.5625 Combine like terms: -0.793036096 + 0.5625 = -0.230536096 x = -0.230536096 Simplifying x = -0.230536096Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.355536096, -0.230536096}
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