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Simplifying (2.2(x + -4))(x + -4) * 2 = 320 Reorder the terms: (2.2(-4 + x))(x + -4) * 2 = 320 ((-4 * 2.2 + x * 2.2))(x + -4) * 2 = 320 ((-8.8 + 2.2x))(x + -4) * 2 = 320 Reorder the terms: (-8.8 + 2.2x)(-4 + x) * 2 = 320 Reorder the terms for easier multiplication: 2(-8.8 + 2.2x)(-4 + x) = 320 Multiply (-8.8 + 2.2x) * (-4 + x) 2(-8.8(-4 + x) + 2.2x * (-4 + x)) = 320 2((-4 * -8.8 + x * -8.8) + 2.2x * (-4 + x)) = 320 2((35.2 + -8.8x) + 2.2x * (-4 + x)) = 320 2(35.2 + -8.8x + (-4 * 2.2x + x * 2.2x)) = 320 2(35.2 + -8.8x + (-8.8x + 2.2x2)) = 320 Combine like terms: -8.8x + -8.8x = -17.6x 2(35.2 + -17.6x + 2.2x2) = 320 (35.2 * 2 + -17.6x * 2 + 2.2x2 * 2) = 320 (70.4 + -35.2x + 4.4x2) = 320 Solving 70.4 + -35.2x + 4.4x2 = 320 Solving for variable 'x'. Reorder the terms: 70.4 + -320 + -35.2x + 4.4x2 = 320 + -320 Combine like terms: 70.4 + -320 = -249.6 -249.6 + -35.2x + 4.4x2 = 320 + -320 Combine like terms: 320 + -320 = 0 -249.6 + -35.2x + 4.4x2 = 0 Begin completing the square. Divide all terms by 4.4 the coefficient of the squared term: Divide each side by '4.4'. -56.72727273 + -8x + x2 = 0 Move the constant term to the right: Add '56.72727273' to each side of the equation. -56.72727273 + -8x + 56.72727273 + x2 = 0 + 56.72727273 Reorder the terms: -56.72727273 + 56.72727273 + -8x + x2 = 0 + 56.72727273 Combine like terms: -56.72727273 + 56.72727273 = 0.00000000 0.00000000 + -8x + x2 = 0 + 56.72727273 -8x + x2 = 0 + 56.72727273 Combine like terms: 0 + 56.72727273 = 56.72727273 -8x + x2 = 56.72727273 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 56.72727273 + 16 Reorder the terms: 16 + -8x + x2 = 56.72727273 + 16 Combine like terms: 56.72727273 + 16 = 72.72727273 16 + -8x + x2 = 72.72727273 Factor a perfect square on the left side: (x + -4)(x + -4) = 72.72727273 Calculate the square root of the right side: 8.528028654 Break this problem into two subproblems by setting (x + -4) equal to 8.528028654 and -8.528028654.Subproblem 1
x + -4 = 8.528028654 Simplifying x + -4 = 8.528028654 Reorder the terms: -4 + x = 8.528028654 Solving -4 + x = 8.528028654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 8.528028654 + 4 Combine like terms: -4 + 4 = 0 0 + x = 8.528028654 + 4 x = 8.528028654 + 4 Combine like terms: 8.528028654 + 4 = 12.528028654 x = 12.528028654 Simplifying x = 12.528028654Subproblem 2
x + -4 = -8.528028654 Simplifying x + -4 = -8.528028654 Reorder the terms: -4 + x = -8.528028654 Solving -4 + x = -8.528028654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -8.528028654 + 4 Combine like terms: -4 + 4 = 0 0 + x = -8.528028654 + 4 x = -8.528028654 + 4 Combine like terms: -8.528028654 + 4 = -4.528028654 x = -4.528028654 Simplifying x = -4.528028654Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.528028654, -4.528028654}
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