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Simplifying (2.2(x + -4))(x + -4) * 2 = 360 Reorder the terms: (2.2(-4 + x))(x + -4) * 2 = 360 ((-4 * 2.2 + x * 2.2))(x + -4) * 2 = 360 ((-8.8 + 2.2x))(x + -4) * 2 = 360 Reorder the terms: (-8.8 + 2.2x)(-4 + x) * 2 = 360 Reorder the terms for easier multiplication: 2(-8.8 + 2.2x)(-4 + x) = 360 Multiply (-8.8 + 2.2x) * (-4 + x) 2(-8.8(-4 + x) + 2.2x * (-4 + x)) = 360 2((-4 * -8.8 + x * -8.8) + 2.2x * (-4 + x)) = 360 2((35.2 + -8.8x) + 2.2x * (-4 + x)) = 360 2(35.2 + -8.8x + (-4 * 2.2x + x * 2.2x)) = 360 2(35.2 + -8.8x + (-8.8x + 2.2x2)) = 360 Combine like terms: -8.8x + -8.8x = -17.6x 2(35.2 + -17.6x + 2.2x2) = 360 (35.2 * 2 + -17.6x * 2 + 2.2x2 * 2) = 360 (70.4 + -35.2x + 4.4x2) = 360 Solving 70.4 + -35.2x + 4.4x2 = 360 Solving for variable 'x'. Reorder the terms: 70.4 + -360 + -35.2x + 4.4x2 = 360 + -360 Combine like terms: 70.4 + -360 = -289.6 -289.6 + -35.2x + 4.4x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -289.6 + -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'. -65.81818182 + -8x + x2 = 0 Move the constant term to the right: Add '65.81818182' to each side of the equation. -65.81818182 + -8x + 65.81818182 + x2 = 0 + 65.81818182 Reorder the terms: -65.81818182 + 65.81818182 + -8x + x2 = 0 + 65.81818182 Combine like terms: -65.81818182 + 65.81818182 = 0.00000000 0.00000000 + -8x + x2 = 0 + 65.81818182 -8x + x2 = 0 + 65.81818182 Combine like terms: 0 + 65.81818182 = 65.81818182 -8x + x2 = 65.81818182 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 = 65.81818182 + 16 Reorder the terms: 16 + -8x + x2 = 65.81818182 + 16 Combine like terms: 65.81818182 + 16 = 81.81818182 16 + -8x + x2 = 81.81818182 Factor a perfect square on the left side: (x + -4)(x + -4) = 81.81818182 Calculate the square root of the right side: 9.045340337 Break this problem into two subproblems by setting (x + -4) equal to 9.045340337 and -9.045340337.Subproblem 1
x + -4 = 9.045340337 Simplifying x + -4 = 9.045340337 Reorder the terms: -4 + x = 9.045340337 Solving -4 + x = 9.045340337 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 = 9.045340337 + 4 Combine like terms: -4 + 4 = 0 0 + x = 9.045340337 + 4 x = 9.045340337 + 4 Combine like terms: 9.045340337 + 4 = 13.045340337 x = 13.045340337 Simplifying x = 13.045340337Subproblem 2
x + -4 = -9.045340337 Simplifying x + -4 = -9.045340337 Reorder the terms: -4 + x = -9.045340337 Solving -4 + x = -9.045340337 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 = -9.045340337 + 4 Combine like terms: -4 + 4 = 0 0 + x = -9.045340337 + 4 x = -9.045340337 + 4 Combine like terms: -9.045340337 + 4 = -5.045340337 x = -5.045340337 Simplifying x = -5.045340337Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.045340337, -5.045340337}
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