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Simplifying 16x2 = 3x + 4 Reorder the terms: 16x2 = 4 + 3x Solving 16x2 = 4 + 3x Solving for variable 'x'. Reorder the terms: -4 + -3x + 16x2 = 4 + 3x + -4 + -3x Reorder the terms: -4 + -3x + 16x2 = 4 + -4 + 3x + -3x Combine like terms: 4 + -4 = 0 -4 + -3x + 16x2 = 0 + 3x + -3x -4 + -3x + 16x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -4 + -3x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.25 + -0.1875x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -0.1875x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -0.1875x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -0.1875x + x2 = 0 + 0.25 -0.1875x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -0.1875x + x2 = 0.25 The x term is -0.1875x. Take half its coefficient (-0.09375). Square it (0.0087890625) and add it to both sides. Add '0.0087890625' to each side of the equation. -0.1875x + 0.0087890625 + x2 = 0.25 + 0.0087890625 Reorder the terms: 0.0087890625 + -0.1875x + x2 = 0.25 + 0.0087890625 Combine like terms: 0.25 + 0.0087890625 = 0.2587890625 0.0087890625 + -0.1875x + x2 = 0.2587890625 Factor a perfect square on the left side: (x + -0.09375)(x + -0.09375) = 0.2587890625 Calculate the square root of the right side: 0.508713144 Break this problem into two subproblems by setting (x + -0.09375) equal to 0.508713144 and -0.508713144.Subproblem 1
x + -0.09375 = 0.508713144 Simplifying x + -0.09375 = 0.508713144 Reorder the terms: -0.09375 + x = 0.508713144 Solving -0.09375 + x = 0.508713144 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.09375' to each side of the equation. -0.09375 + 0.09375 + x = 0.508713144 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + x = 0.508713144 + 0.09375 x = 0.508713144 + 0.09375 Combine like terms: 0.508713144 + 0.09375 = 0.602463144 x = 0.602463144 Simplifying x = 0.602463144Subproblem 2
x + -0.09375 = -0.508713144 Simplifying x + -0.09375 = -0.508713144 Reorder the terms: -0.09375 + x = -0.508713144 Solving -0.09375 + x = -0.508713144 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.09375' to each side of the equation. -0.09375 + 0.09375 + x = -0.508713144 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + x = -0.508713144 + 0.09375 x = -0.508713144 + 0.09375 Combine like terms: -0.508713144 + 0.09375 = -0.414963144 x = -0.414963144 Simplifying x = -0.414963144Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.602463144, -0.414963144}
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