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Simplifying -16x2 + 112x + 5 = 0 Reorder the terms: 5 + 112x + -16x2 = 0 Solving 5 + 112x + -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 + -7x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -7x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -7x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -7x + x2 = 0 + 0.3125 -7x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -7x + x2 = 0.3125 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 0.3125 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 0.3125 + 12.25 Combine like terms: 0.3125 + 12.25 = 12.5625 12.25 + -7x + x2 = 12.5625 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (x + -3.5) equal to 3.54436172 and -3.54436172.Subproblem 1
x + -3.5 = 3.54436172 Simplifying x + -3.5 = 3.54436172 Reorder the terms: -3.5 + x = 3.54436172 Solving -3.5 + x = 3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.54436172 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.54436172 + 3.5 x = 3.54436172 + 3.5 Combine like terms: 3.54436172 + 3.5 = 7.04436172 x = 7.04436172 Simplifying x = 7.04436172Subproblem 2
x + -3.5 = -3.54436172 Simplifying x + -3.5 = -3.54436172 Reorder the terms: -3.5 + x = -3.54436172 Solving -3.5 + x = -3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.54436172 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.54436172 + 3.5 x = -3.54436172 + 3.5 Combine like terms: -3.54436172 + 3.5 = -0.04436172 x = -0.04436172 Simplifying x = -0.04436172Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.04436172, -0.04436172}
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