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Simplifying -16x2 + 50x + 7 = 0 Reorder the terms: 7 + 50x + -16x2 = 0 Solving 7 + 50x + -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 + -3.125x + x2 = 0 Move the constant term to the right: Add '0.4375' to each side of the equation. -0.4375 + -3.125x + 0.4375 + x2 = 0 + 0.4375 Reorder the terms: -0.4375 + 0.4375 + -3.125x + x2 = 0 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + -3.125x + x2 = 0 + 0.4375 -3.125x + x2 = 0 + 0.4375 Combine like terms: 0 + 0.4375 = 0.4375 -3.125x + x2 = 0.4375 The x term is -3.125x. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125x + 2.44140625 + x2 = 0.4375 + 2.44140625 Reorder the terms: 2.44140625 + -3.125x + x2 = 0.4375 + 2.44140625 Combine like terms: 0.4375 + 2.44140625 = 2.87890625 2.44140625 + -3.125x + x2 = 2.87890625 Factor a perfect square on the left side: (x + -1.5625)(x + -1.5625) = 2.87890625 Calculate the square root of the right side: 1.696733995 Break this problem into two subproblems by setting (x + -1.5625) equal to 1.696733995 and -1.696733995.Subproblem 1
x + -1.5625 = 1.696733995 Simplifying x + -1.5625 = 1.696733995 Reorder the terms: -1.5625 + x = 1.696733995 Solving -1.5625 + x = 1.696733995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = 1.696733995 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = 1.696733995 + 1.5625 x = 1.696733995 + 1.5625 Combine like terms: 1.696733995 + 1.5625 = 3.259233995 x = 3.259233995 Simplifying x = 3.259233995Subproblem 2
x + -1.5625 = -1.696733995 Simplifying x + -1.5625 = -1.696733995 Reorder the terms: -1.5625 + x = -1.696733995 Solving -1.5625 + x = -1.696733995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = -1.696733995 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = -1.696733995 + 1.5625 x = -1.696733995 + 1.5625 Combine like terms: -1.696733995 + 1.5625 = -0.134233995 x = -0.134233995 Simplifying x = -0.134233995Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.259233995, -0.134233995}
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