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Simplifying 3x + 16 = 4x(8x + -7) Reorder the terms: 16 + 3x = 4x(8x + -7) Reorder the terms: 16 + 3x = 4x(-7 + 8x) 16 + 3x = (-7 * 4x + 8x * 4x) 16 + 3x = (-28x + 32x2) Solving 16 + 3x = -28x + 32x2 Solving for variable 'x'. Combine like terms: 3x + 28x = 31x 16 + 31x + -32x2 = -28x + 32x2 + 28x + -32x2 Reorder the terms: 16 + 31x + -32x2 = -28x + 28x + 32x2 + -32x2 Combine like terms: -28x + 28x = 0 16 + 31x + -32x2 = 0 + 32x2 + -32x2 16 + 31x + -32x2 = 32x2 + -32x2 Combine like terms: 32x2 + -32x2 = 0 16 + 31x + -32x2 = 0 Begin completing the square. Divide all terms by -32 the coefficient of the squared term: Divide each side by '-32'. -0.5 + -0.96875x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.96875x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.96875x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.96875x + x2 = 0 + 0.5 -0.96875x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.96875x + x2 = 0.5 The x term is -0.96875x. Take half its coefficient (-0.484375). Square it (0.2346191406) and add it to both sides. Add '0.2346191406' to each side of the equation. -0.96875x + 0.2346191406 + x2 = 0.5 + 0.2346191406 Reorder the terms: 0.2346191406 + -0.96875x + x2 = 0.5 + 0.2346191406 Combine like terms: 0.5 + 0.2346191406 = 0.7346191406 0.2346191406 + -0.96875x + x2 = 0.7346191406 Factor a perfect square on the left side: (x + -0.484375)(x + -0.484375) = 0.7346191406 Calculate the square root of the right side: 0.857099259 Break this problem into two subproblems by setting (x + -0.484375) equal to 0.857099259 and -0.857099259.Subproblem 1
x + -0.484375 = 0.857099259 Simplifying x + -0.484375 = 0.857099259 Reorder the terms: -0.484375 + x = 0.857099259 Solving -0.484375 + x = 0.857099259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.484375' to each side of the equation. -0.484375 + 0.484375 + x = 0.857099259 + 0.484375 Combine like terms: -0.484375 + 0.484375 = 0.000000 0.000000 + x = 0.857099259 + 0.484375 x = 0.857099259 + 0.484375 Combine like terms: 0.857099259 + 0.484375 = 1.341474259 x = 1.341474259 Simplifying x = 1.341474259Subproblem 2
x + -0.484375 = -0.857099259 Simplifying x + -0.484375 = -0.857099259 Reorder the terms: -0.484375 + x = -0.857099259 Solving -0.484375 + x = -0.857099259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.484375' to each side of the equation. -0.484375 + 0.484375 + x = -0.857099259 + 0.484375 Combine like terms: -0.484375 + 0.484375 = 0.000000 0.000000 + x = -0.857099259 + 0.484375 x = -0.857099259 + 0.484375 Combine like terms: -0.857099259 + 0.484375 = -0.372724259 x = -0.372724259 Simplifying x = -0.372724259Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.341474259, -0.372724259}
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