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Simplifying 25 = 16x2 + 35x + 7 Reorder the terms: 25 = 7 + 35x + 16x2 Solving 25 = 7 + 35x + 16x2 Solving for variable 'x'. Combine like terms: 25 + -7 = 18 18 + -35x + -16x2 = 7 + 35x + 16x2 + -7 + -35x + -16x2 Reorder the terms: 18 + -35x + -16x2 = 7 + -7 + 35x + -35x + 16x2 + -16x2 Combine like terms: 7 + -7 = 0 18 + -35x + -16x2 = 0 + 35x + -35x + 16x2 + -16x2 18 + -35x + -16x2 = 35x + -35x + 16x2 + -16x2 Combine like terms: 35x + -35x = 0 18 + -35x + -16x2 = 0 + 16x2 + -16x2 18 + -35x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 18 + -35x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -1.125 + 2.1875x + x2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + 2.1875x + 1.125 + x2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + 2.1875x + x2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + 2.1875x + x2 = 0 + 1.125 2.1875x + x2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 2.1875x + x2 = 1.125 The x term is 2.1875x. Take half its coefficient (1.09375). Square it (1.196289063) and add it to both sides. Add '1.196289063' to each side of the equation. 2.1875x + 1.196289063 + x2 = 1.125 + 1.196289063 Reorder the terms: 1.196289063 + 2.1875x + x2 = 1.125 + 1.196289063 Combine like terms: 1.125 + 1.196289063 = 2.321289063 1.196289063 + 2.1875x + x2 = 2.321289063 Factor a perfect square on the left side: (x + 1.09375)(x + 1.09375) = 2.321289063 Calculate the square root of the right side: 1.523577718 Break this problem into two subproblems by setting (x + 1.09375) equal to 1.523577718 and -1.523577718.Subproblem 1
x + 1.09375 = 1.523577718 Simplifying x + 1.09375 = 1.523577718 Reorder the terms: 1.09375 + x = 1.523577718 Solving 1.09375 + x = 1.523577718 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.09375' to each side of the equation. 1.09375 + -1.09375 + x = 1.523577718 + -1.09375 Combine like terms: 1.09375 + -1.09375 = 0.00000 0.00000 + x = 1.523577718 + -1.09375 x = 1.523577718 + -1.09375 Combine like terms: 1.523577718 + -1.09375 = 0.429827718 x = 0.429827718 Simplifying x = 0.429827718Subproblem 2
x + 1.09375 = -1.523577718 Simplifying x + 1.09375 = -1.523577718 Reorder the terms: 1.09375 + x = -1.523577718 Solving 1.09375 + x = -1.523577718 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.09375' to each side of the equation. 1.09375 + -1.09375 + x = -1.523577718 + -1.09375 Combine like terms: 1.09375 + -1.09375 = 0.00000 0.00000 + x = -1.523577718 + -1.09375 x = -1.523577718 + -1.09375 Combine like terms: -1.523577718 + -1.09375 = -2.617327718 x = -2.617327718 Simplifying x = -2.617327718Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.429827718, -2.617327718}
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