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Simplifying 2(x + -35.24)(x + 27.24) = 0 Reorder the terms: 2(-35.24 + x)(x + 27.24) = 0 Reorder the terms: 2(-35.24 + x)(27.24 + x) = 0 Multiply (-35.24 + x) * (27.24 + x) 2(-35.24(27.24 + x) + x(27.24 + x)) = 0 2((27.24 * -35.24 + x * -35.24) + x(27.24 + x)) = 0 2((-959.9376 + -35.24x) + x(27.24 + x)) = 0 2(-959.9376 + -35.24x + (27.24 * x + x * x)) = 0 2(-959.9376 + -35.24x + (27.24x + x2)) = 0 Combine like terms: -35.24x + 27.24x = -8x 2(-959.9376 + -8x + x2) = 0 (-959.9376 * 2 + -8x * 2 + x2 * 2) = 0 (-1919.8752 + -16x + 2x2) = 0 Solving -1919.8752 + -16x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -959.9376 + -8x + x2 = 0 Move the constant term to the right: Add '959.9376' to each side of the equation. -959.9376 + -8x + 959.9376 + x2 = 0 + 959.9376 Reorder the terms: -959.9376 + 959.9376 + -8x + x2 = 0 + 959.9376 Combine like terms: -959.9376 + 959.9376 = 0.0000 0.0000 + -8x + x2 = 0 + 959.9376 -8x + x2 = 0 + 959.9376 Combine like terms: 0 + 959.9376 = 959.9376 -8x + x2 = 959.9376 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 = 959.9376 + 16 Reorder the terms: 16 + -8x + x2 = 959.9376 + 16 Combine like terms: 959.9376 + 16 = 975.9376 16 + -8x + x2 = 975.9376 Factor a perfect square on the left side: (x + -4)(x + -4) = 975.9376 Calculate the square root of the right side: 31.24 Break this problem into two subproblems by setting (x + -4) equal to 31.24 and -31.24.Subproblem 1
x + -4 = 31.24 Simplifying x + -4 = 31.24 Reorder the terms: -4 + x = 31.24 Solving -4 + x = 31.24 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 = 31.24 + 4 Combine like terms: -4 + 4 = 0 0 + x = 31.24 + 4 x = 31.24 + 4 Combine like terms: 31.24 + 4 = 35.24 x = 35.24 Simplifying x = 35.24Subproblem 2
x + -4 = -31.24 Simplifying x + -4 = -31.24 Reorder the terms: -4 + x = -31.24 Solving -4 + x = -31.24 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 = -31.24 + 4 Combine like terms: -4 + 4 = 0 0 + x = -31.24 + 4 x = -31.24 + 4 Combine like terms: -31.24 + 4 = -27.24 x = -27.24 Simplifying x = -27.24Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.24, -27.24}
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