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Simplifying 16x2 + -45x + 7 = 0 Reorder the terms: 7 + -45x + 16x2 = 0 Solving 7 + -45x + 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'. 0.4375 + -2.8125x + x2 = 0 Move the constant term to the right: Add '-0.4375' to each side of the equation. 0.4375 + -2.8125x + -0.4375 + x2 = 0 + -0.4375 Reorder the terms: 0.4375 + -0.4375 + -2.8125x + x2 = 0 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + -2.8125x + x2 = 0 + -0.4375 -2.8125x + x2 = 0 + -0.4375 Combine like terms: 0 + -0.4375 = -0.4375 -2.8125x + x2 = -0.4375 The x term is -2.8125x. Take half its coefficient (-1.40625). Square it (1.977539063) and add it to both sides. Add '1.977539063' to each side of the equation. -2.8125x + 1.977539063 + x2 = -0.4375 + 1.977539063 Reorder the terms: 1.977539063 + -2.8125x + x2 = -0.4375 + 1.977539063 Combine like terms: -0.4375 + 1.977539063 = 1.540039063 1.977539063 + -2.8125x + x2 = 1.540039063 Factor a perfect square on the left side: (x + -1.40625)(x + -1.40625) = 1.540039063 Calculate the square root of the right side: 1.240983103 Break this problem into two subproblems by setting (x + -1.40625) equal to 1.240983103 and -1.240983103.Subproblem 1
x + -1.40625 = 1.240983103 Simplifying x + -1.40625 = 1.240983103 Reorder the terms: -1.40625 + x = 1.240983103 Solving -1.40625 + x = 1.240983103 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + x = 1.240983103 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + x = 1.240983103 + 1.40625 x = 1.240983103 + 1.40625 Combine like terms: 1.240983103 + 1.40625 = 2.647233103 x = 2.647233103 Simplifying x = 2.647233103Subproblem 2
x + -1.40625 = -1.240983103 Simplifying x + -1.40625 = -1.240983103 Reorder the terms: -1.40625 + x = -1.240983103 Solving -1.40625 + x = -1.240983103 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + x = -1.240983103 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + x = -1.240983103 + 1.40625 x = -1.240983103 + 1.40625 Combine like terms: -1.240983103 + 1.40625 = 0.165266897 x = 0.165266897 Simplifying x = 0.165266897Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.647233103, 0.165266897}
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