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Simplifying (14.5 + -1x)(-7 + -1x) = 0 Multiply (14.5 + -1x) * (-7 + -1x) (14.5(-7 + -1x) + -1x * (-7 + -1x)) = 0 ((-7 * 14.5 + -1x * 14.5) + -1x * (-7 + -1x)) = 0 ((-101.5 + -14.5x) + -1x * (-7 + -1x)) = 0 (-101.5 + -14.5x + (-7 * -1x + -1x * -1x)) = 0 (-101.5 + -14.5x + (7x + 1x2)) = 0 Combine like terms: -14.5x + 7x = -7.5x (-101.5 + -7.5x + 1x2) = 0 Solving -101.5 + -7.5x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '101.5' to each side of the equation. -101.5 + -7.5x + 101.5 + x2 = 0 + 101.5 Reorder the terms: -101.5 + 101.5 + -7.5x + x2 = 0 + 101.5 Combine like terms: -101.5 + 101.5 = 0.0 0.0 + -7.5x + x2 = 0 + 101.5 -7.5x + x2 = 0 + 101.5 Combine like terms: 0 + 101.5 = 101.5 -7.5x + x2 = 101.5 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = 101.5 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = 101.5 + 14.0625 Combine like terms: 101.5 + 14.0625 = 115.5625 14.0625 + -7.5x + x2 = 115.5625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 115.5625 Calculate the square root of the right side: 10.75 Break this problem into two subproblems by setting (x + -3.75) equal to 10.75 and -10.75.Subproblem 1
x + -3.75 = 10.75 Simplifying x + -3.75 = 10.75 Reorder the terms: -3.75 + x = 10.75 Solving -3.75 + x = 10.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 10.75 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 10.75 + 3.75 x = 10.75 + 3.75 Combine like terms: 10.75 + 3.75 = 14.5 x = 14.5 Simplifying x = 14.5Subproblem 2
x + -3.75 = -10.75 Simplifying x + -3.75 = -10.75 Reorder the terms: -3.75 + x = -10.75 Solving -3.75 + x = -10.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -10.75 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -10.75 + 3.75 x = -10.75 + 3.75 Combine like terms: -10.75 + 3.75 = -7 x = -7 Simplifying x = -7Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.5, -7}
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