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Simplifying -2x(x + 4) = 2(-2x + -8) + 5x Reorder the terms: -2x(4 + x) = 2(-2x + -8) + 5x (4 * -2x + x * -2x) = 2(-2x + -8) + 5x (-8x + -2x2) = 2(-2x + -8) + 5x Reorder the terms: -8x + -2x2 = 2(-8 + -2x) + 5x -8x + -2x2 = (-8 * 2 + -2x * 2) + 5x -8x + -2x2 = (-16 + -4x) + 5x Combine like terms: -4x + 5x = 1x -8x + -2x2 = -16 + 1x Solving -8x + -2x2 = -16 + 1x Solving for variable 'x'. Reorder the terms: 16 + -8x + -1x + -2x2 = -16 + 1x + 16 + -1x Combine like terms: -8x + -1x = -9x 16 + -9x + -2x2 = -16 + 1x + 16 + -1x Reorder the terms: 16 + -9x + -2x2 = -16 + 16 + 1x + -1x Combine like terms: -16 + 16 = 0 16 + -9x + -2x2 = 0 + 1x + -1x 16 + -9x + -2x2 = 1x + -1x Combine like terms: 1x + -1x = 0 16 + -9x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -8 + 4.5x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 4.5x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 4.5x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 4.5x + x2 = 0 + 8 4.5x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 4.5x + x2 = 8 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 8 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 8 + 5.0625 Combine like terms: 8 + 5.0625 = 13.0625 5.0625 + 4.5x + x2 = 13.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 13.0625 Calculate the square root of the right side: 3.614208074 Break this problem into two subproblems by setting (x + 2.25) equal to 3.614208074 and -3.614208074.Subproblem 1
x + 2.25 = 3.614208074 Simplifying x + 2.25 = 3.614208074 Reorder the terms: 2.25 + x = 3.614208074 Solving 2.25 + x = 3.614208074 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 3.614208074 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 3.614208074 + -2.25 x = 3.614208074 + -2.25 Combine like terms: 3.614208074 + -2.25 = 1.364208074 x = 1.364208074 Simplifying x = 1.364208074Subproblem 2
x + 2.25 = -3.614208074 Simplifying x + 2.25 = -3.614208074 Reorder the terms: 2.25 + x = -3.614208074 Solving 2.25 + x = -3.614208074 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -3.614208074 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -3.614208074 + -2.25 x = -3.614208074 + -2.25 Combine like terms: -3.614208074 + -2.25 = -5.864208074 x = -5.864208074 Simplifying x = -5.864208074Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.364208074, -5.864208074}
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