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Simplifying (14 + -0.8x)(5 + -0.5x) = 0 Multiply (14 + -0.8x) * (5 + -0.5x) (14(5 + -0.5x) + -0.8x * (5 + -0.5x)) = 0 ((5 * 14 + -0.5x * 14) + -0.8x * (5 + -0.5x)) = 0 ((70 + -7x) + -0.8x * (5 + -0.5x)) = 0 (70 + -7x + (5 * -0.8x + -0.5x * -0.8x)) = 0 (70 + -7x + (-4x + 0.4x2)) = 0 Combine like terms: -7x + -4x = -11x (70 + -11x + 0.4x2) = 0 Solving 70 + -11x + 0.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. 175 + -27.5x + x2 = 0 Move the constant term to the right: Add '-175' to each side of the equation. 175 + -27.5x + -175 + x2 = 0 + -175 Reorder the terms: 175 + -175 + -27.5x + x2 = 0 + -175 Combine like terms: 175 + -175 = 0 0 + -27.5x + x2 = 0 + -175 -27.5x + x2 = 0 + -175 Combine like terms: 0 + -175 = -175 -27.5x + x2 = -175 The x term is -27.5x. Take half its coefficient (-13.75). Square it (189.0625) and add it to both sides. Add '189.0625' to each side of the equation. -27.5x + 189.0625 + x2 = -175 + 189.0625 Reorder the terms: 189.0625 + -27.5x + x2 = -175 + 189.0625 Combine like terms: -175 + 189.0625 = 14.0625 189.0625 + -27.5x + x2 = 14.0625 Factor a perfect square on the left side: (x + -13.75)(x + -13.75) = 14.0625 Calculate the square root of the right side: 3.75 Break this problem into two subproblems by setting (x + -13.75) equal to 3.75 and -3.75.Subproblem 1
x + -13.75 = 3.75 Simplifying x + -13.75 = 3.75 Reorder the terms: -13.75 + x = 3.75 Solving -13.75 + x = 3.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.75' to each side of the equation. -13.75 + 13.75 + x = 3.75 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + x = 3.75 + 13.75 x = 3.75 + 13.75 Combine like terms: 3.75 + 13.75 = 17.5 x = 17.5 Simplifying x = 17.5Subproblem 2
x + -13.75 = -3.75 Simplifying x + -13.75 = -3.75 Reorder the terms: -13.75 + x = -3.75 Solving -13.75 + x = -3.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.75' to each side of the equation. -13.75 + 13.75 + x = -3.75 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + x = -3.75 + 13.75 x = -3.75 + 13.75 Combine like terms: -3.75 + 13.75 = 10 x = 10 Simplifying x = 10Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.5, 10}
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