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Simplifying (9 + -0.8x)(5 + -0.5x) = 0 Multiply (9 + -0.8x) * (5 + -0.5x) (9(5 + -0.5x) + -0.8x * (5 + -0.5x)) = 0 ((5 * 9 + -0.5x * 9) + -0.8x * (5 + -0.5x)) = 0 ((45 + -4.5x) + -0.8x * (5 + -0.5x)) = 0 (45 + -4.5x + (5 * -0.8x + -0.5x * -0.8x)) = 0 (45 + -4.5x + (-4x + 0.4x2)) = 0 Combine like terms: -4.5x + -4x = -8.5x (45 + -8.5x + 0.4x2) = 0 Solving 45 + -8.5x + 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'. 112.5 + -21.25x + x2 = 0 Move the constant term to the right: Add '-112.5' to each side of the equation. 112.5 + -21.25x + -112.5 + x2 = 0 + -112.5 Reorder the terms: 112.5 + -112.5 + -21.25x + x2 = 0 + -112.5 Combine like terms: 112.5 + -112.5 = 0.0 0.0 + -21.25x + x2 = 0 + -112.5 -21.25x + x2 = 0 + -112.5 Combine like terms: 0 + -112.5 = -112.5 -21.25x + x2 = -112.5 The x term is -21.25x. Take half its coefficient (-10.625). Square it (112.890625) and add it to both sides. Add '112.890625' to each side of the equation. -21.25x + 112.890625 + x2 = -112.5 + 112.890625 Reorder the terms: 112.890625 + -21.25x + x2 = -112.5 + 112.890625 Combine like terms: -112.5 + 112.890625 = 0.390625 112.890625 + -21.25x + x2 = 0.390625 Factor a perfect square on the left side: (x + -10.625)(x + -10.625) = 0.390625 Calculate the square root of the right side: 0.625 Break this problem into two subproblems by setting (x + -10.625) equal to 0.625 and -0.625.Subproblem 1
x + -10.625 = 0.625 Simplifying x + -10.625 = 0.625 Reorder the terms: -10.625 + x = 0.625 Solving -10.625 + x = 0.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.625' to each side of the equation. -10.625 + 10.625 + x = 0.625 + 10.625 Combine like terms: -10.625 + 10.625 = 0.000 0.000 + x = 0.625 + 10.625 x = 0.625 + 10.625 Combine like terms: 0.625 + 10.625 = 11.25 x = 11.25 Simplifying x = 11.25Subproblem 2
x + -10.625 = -0.625 Simplifying x + -10.625 = -0.625 Reorder the terms: -10.625 + x = -0.625 Solving -10.625 + x = -0.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.625' to each side of the equation. -10.625 + 10.625 + x = -0.625 + 10.625 Combine like terms: -10.625 + 10.625 = 0.000 0.000 + x = -0.625 + 10.625 x = -0.625 + 10.625 Combine like terms: -0.625 + 10.625 = 10 x = 10 Simplifying x = 10Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.25, 10}
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