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Simplifying 2x + -1 + 6(2x + 1) = 16x(2x + -7) Reorder the terms: 2x + -1 + 6(1 + 2x) = 16x(2x + -7) 2x + -1 + (1 * 6 + 2x * 6) = 16x(2x + -7) 2x + -1 + (6 + 12x) = 16x(2x + -7) Reorder the terms: -1 + 6 + 2x + 12x = 16x(2x + -7) Combine like terms: -1 + 6 = 5 5 + 2x + 12x = 16x(2x + -7) Combine like terms: 2x + 12x = 14x 5 + 14x = 16x(2x + -7) Reorder the terms: 5 + 14x = 16x(-7 + 2x) 5 + 14x = (-7 * 16x + 2x * 16x) 5 + 14x = (-112x + 32x2) Solving 5 + 14x = -112x + 32x2 Solving for variable 'x'. Combine like terms: 14x + 112x = 126x 5 + 126x + -32x2 = -112x + 32x2 + 112x + -32x2 Reorder the terms: 5 + 126x + -32x2 = -112x + 112x + 32x2 + -32x2 Combine like terms: -112x + 112x = 0 5 + 126x + -32x2 = 0 + 32x2 + -32x2 5 + 126x + -32x2 = 32x2 + -32x2 Combine like terms: 32x2 + -32x2 = 0 5 + 126x + -32x2 = 0 Begin completing the square. Divide all terms by -32 the coefficient of the squared term: Divide each side by '-32'. -0.15625 + -3.9375x + x2 = 0 Move the constant term to the right: Add '0.15625' to each side of the equation. -0.15625 + -3.9375x + 0.15625 + x2 = 0 + 0.15625 Reorder the terms: -0.15625 + 0.15625 + -3.9375x + x2 = 0 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + -3.9375x + x2 = 0 + 0.15625 -3.9375x + x2 = 0 + 0.15625 Combine like terms: 0 + 0.15625 = 0.15625 -3.9375x + x2 = 0.15625 The x term is -3.9375x. Take half its coefficient (-1.96875). Square it (3.875976563) and add it to both sides. Add '3.875976563' to each side of the equation. -3.9375x + 3.875976563 + x2 = 0.15625 + 3.875976563 Reorder the terms: 3.875976563 + -3.9375x + x2 = 0.15625 + 3.875976563 Combine like terms: 0.15625 + 3.875976563 = 4.032226563 3.875976563 + -3.9375x + x2 = 4.032226563 Factor a perfect square on the left side: (x + -1.96875)(x + -1.96875) = 4.032226563 Calculate the square root of the right side: 2.008040478 Break this problem into two subproblems by setting (x + -1.96875) equal to 2.008040478 and -2.008040478.Subproblem 1
x + -1.96875 = 2.008040478 Simplifying x + -1.96875 = 2.008040478 Reorder the terms: -1.96875 + x = 2.008040478 Solving -1.96875 + x = 2.008040478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.96875' to each side of the equation. -1.96875 + 1.96875 + x = 2.008040478 + 1.96875 Combine like terms: -1.96875 + 1.96875 = 0.00000 0.00000 + x = 2.008040478 + 1.96875 x = 2.008040478 + 1.96875 Combine like terms: 2.008040478 + 1.96875 = 3.976790478 x = 3.976790478 Simplifying x = 3.976790478Subproblem 2
x + -1.96875 = -2.008040478 Simplifying x + -1.96875 = -2.008040478 Reorder the terms: -1.96875 + x = -2.008040478 Solving -1.96875 + x = -2.008040478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.96875' to each side of the equation. -1.96875 + 1.96875 + x = -2.008040478 + 1.96875 Combine like terms: -1.96875 + 1.96875 = 0.00000 0.00000 + x = -2.008040478 + 1.96875 x = -2.008040478 + 1.96875 Combine like terms: -2.008040478 + 1.96875 = -0.039290478 x = -0.039290478 Simplifying x = -0.039290478Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.976790478, -0.039290478}
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