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Simplifying 2x(x + -4) + -9 = 4(3 + -1x) Reorder the terms: 2x(-4 + x) + -9 = 4(3 + -1x) (-4 * 2x + x * 2x) + -9 = 4(3 + -1x) (-8x + 2x2) + -9 = 4(3 + -1x) Reorder the terms: -9 + -8x + 2x2 = 4(3 + -1x) -9 + -8x + 2x2 = (3 * 4 + -1x * 4) -9 + -8x + 2x2 = (12 + -4x) Solving -9 + -8x + 2x2 = 12 + -4x Solving for variable 'x'. Reorder the terms: -9 + -12 + -8x + 4x + 2x2 = 12 + -4x + -12 + 4x Combine like terms: -9 + -12 = -21 -21 + -8x + 4x + 2x2 = 12 + -4x + -12 + 4x Combine like terms: -8x + 4x = -4x -21 + -4x + 2x2 = 12 + -4x + -12 + 4x Reorder the terms: -21 + -4x + 2x2 = 12 + -12 + -4x + 4x Combine like terms: 12 + -12 = 0 -21 + -4x + 2x2 = 0 + -4x + 4x -21 + -4x + 2x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -21 + -4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10.5 + -2x + x2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + -2x + 10.5 + x2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + -2x + x2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + -2x + x2 = 0 + 10.5 -2x + x2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 -2x + x2 = 10.5 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 10.5 + 1 Reorder the terms: 1 + -2x + x2 = 10.5 + 1 Combine like terms: 10.5 + 1 = 11.5 1 + -2x + x2 = 11.5 Factor a perfect square on the left side: (x + -1)(x + -1) = 11.5 Calculate the square root of the right side: 3.391164992 Break this problem into two subproblems by setting (x + -1) equal to 3.391164992 and -3.391164992.Subproblem 1
x + -1 = 3.391164992 Simplifying x + -1 = 3.391164992 Reorder the terms: -1 + x = 3.391164992 Solving -1 + x = 3.391164992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 3.391164992 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.391164992 + 1 x = 3.391164992 + 1 Combine like terms: 3.391164992 + 1 = 4.391164992 x = 4.391164992 Simplifying x = 4.391164992Subproblem 2
x + -1 = -3.391164992 Simplifying x + -1 = -3.391164992 Reorder the terms: -1 + x = -3.391164992 Solving -1 + x = -3.391164992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -3.391164992 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.391164992 + 1 x = -3.391164992 + 1 Combine like terms: -3.391164992 + 1 = -2.391164992 x = -2.391164992 Simplifying x = -2.391164992Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.391164992, -2.391164992}
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