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Simplifying 10 = -16x2 + 25x + 3 Reorder the terms: 10 = 3 + 25x + -16x2 Solving 10 = 3 + 25x + -16x2 Solving for variable 'x'. Combine like terms: 10 + -3 = 7 7 + -25x + 16x2 = 3 + 25x + -16x2 + -3 + -25x + 16x2 Reorder the terms: 7 + -25x + 16x2 = 3 + -3 + 25x + -25x + -16x2 + 16x2 Combine like terms: 3 + -3 = 0 7 + -25x + 16x2 = 0 + 25x + -25x + -16x2 + 16x2 7 + -25x + 16x2 = 25x + -25x + -16x2 + 16x2 Combine like terms: 25x + -25x = 0 7 + -25x + 16x2 = 0 + -16x2 + 16x2 7 + -25x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 7 + -25x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.4375 + -1.5625x + x2 = 0 Move the constant term to the right: Add '-0.4375' to each side of the equation. 0.4375 + -1.5625x + -0.4375 + x2 = 0 + -0.4375 Reorder the terms: 0.4375 + -0.4375 + -1.5625x + x2 = 0 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + -1.5625x + x2 = 0 + -0.4375 -1.5625x + x2 = 0 + -0.4375 Combine like terms: 0 + -0.4375 = -0.4375 -1.5625x + x2 = -0.4375 The x term is -1.5625x. Take half its coefficient (-0.78125). Square it (0.6103515625) and add it to both sides. Add '0.6103515625' to each side of the equation. -1.5625x + 0.6103515625 + x2 = -0.4375 + 0.6103515625 Reorder the terms: 0.6103515625 + -1.5625x + x2 = -0.4375 + 0.6103515625 Combine like terms: -0.4375 + 0.6103515625 = 0.1728515625 0.6103515625 + -1.5625x + x2 = 0.1728515625 Factor a perfect square on the left side: (x + -0.78125)(x + -0.78125) = 0.1728515625 Calculate the square root of the right side: 0.415754209 Break this problem into two subproblems by setting (x + -0.78125) equal to 0.415754209 and -0.415754209.Subproblem 1
x + -0.78125 = 0.415754209 Simplifying x + -0.78125 = 0.415754209 Reorder the terms: -0.78125 + x = 0.415754209 Solving -0.78125 + x = 0.415754209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.78125' to each side of the equation. -0.78125 + 0.78125 + x = 0.415754209 + 0.78125 Combine like terms: -0.78125 + 0.78125 = 0.00000 0.00000 + x = 0.415754209 + 0.78125 x = 0.415754209 + 0.78125 Combine like terms: 0.415754209 + 0.78125 = 1.197004209 x = 1.197004209 Simplifying x = 1.197004209Subproblem 2
x + -0.78125 = -0.415754209 Simplifying x + -0.78125 = -0.415754209 Reorder the terms: -0.78125 + x = -0.415754209 Solving -0.78125 + x = -0.415754209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.78125' to each side of the equation. -0.78125 + 0.78125 + x = -0.415754209 + 0.78125 Combine like terms: -0.78125 + 0.78125 = 0.00000 0.00000 + x = -0.415754209 + 0.78125 x = -0.415754209 + 0.78125 Combine like terms: -0.415754209 + 0.78125 = 0.365495791 x = 0.365495791 Simplifying x = 0.365495791Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.197004209, 0.365495791}
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