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Simplifying (6 + -0.2x)(7 + -0.1x) = 0 Multiply (6 + -0.2x) * (7 + -0.1x) (6(7 + -0.1x) + -0.2x * (7 + -0.1x)) = 0 ((7 * 6 + -0.1x * 6) + -0.2x * (7 + -0.1x)) = 0 ((42 + -0.6x) + -0.2x * (7 + -0.1x)) = 0 (42 + -0.6x + (7 * -0.2x + -0.1x * -0.2x)) = 0 (42 + -0.6x + (-1.4x + 0.02x2)) = 0 Combine like terms: -0.6x + -1.4x = -2x (42 + -2x + 0.02x2) = 0 Solving 42 + -2x + 0.02x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.02 the coefficient of the squared term: Divide each side by '0.02'. 2100 + -100x + x2 = 0 Move the constant term to the right: Add '-2100' to each side of the equation. 2100 + -100x + -2100 + x2 = 0 + -2100 Reorder the terms: 2100 + -2100 + -100x + x2 = 0 + -2100 Combine like terms: 2100 + -2100 = 0 0 + -100x + x2 = 0 + -2100 -100x + x2 = 0 + -2100 Combine like terms: 0 + -2100 = -2100 -100x + x2 = -2100 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -2100 + 2500 Reorder the terms: 2500 + -100x + x2 = -2100 + 2500 Combine like terms: -2100 + 2500 = 400 2500 + -100x + x2 = 400 Factor a perfect square on the left side: (x + -50)(x + -50) = 400 Calculate the square root of the right side: 20 Break this problem into two subproblems by setting (x + -50) equal to 20 and -20.Subproblem 1
x + -50 = 20 Simplifying x + -50 = 20 Reorder the terms: -50 + x = 20 Solving -50 + x = 20 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 20 + 50 Combine like terms: -50 + 50 = 0 0 + x = 20 + 50 x = 20 + 50 Combine like terms: 20 + 50 = 70 x = 70 Simplifying x = 70Subproblem 2
x + -50 = -20 Simplifying x + -50 = -20 Reorder the terms: -50 + x = -20 Solving -50 + x = -20 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -20 + 50 Combine like terms: -50 + 50 = 0 0 + x = -20 + 50 x = -20 + 50 Combine like terms: -20 + 50 = 30 x = 30 Simplifying x = 30Solution
The solution to the problem is based on the solutions from the subproblems. x = {70, 30}
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