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Simplifying (7 + -0.8x)(5 + -0.2x) = 0 Multiply (7 + -0.8x) * (5 + -0.2x) (7(5 + -0.2x) + -0.8x * (5 + -0.2x)) = 0 ((5 * 7 + -0.2x * 7) + -0.8x * (5 + -0.2x)) = 0 ((35 + -1.4x) + -0.8x * (5 + -0.2x)) = 0 (35 + -1.4x + (5 * -0.8x + -0.2x * -0.8x)) = 0 (35 + -1.4x + (-4x + 0.16x2)) = 0 Combine like terms: -1.4x + -4x = -5.4x (35 + -5.4x + 0.16x2) = 0 Solving 35 + -5.4x + 0.16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.16 the coefficient of the squared term: Divide each side by '0.16'. 218.75 + -33.75x + x2 = 0 Move the constant term to the right: Add '-218.75' to each side of the equation. 218.75 + -33.75x + -218.75 + x2 = 0 + -218.75 Reorder the terms: 218.75 + -218.75 + -33.75x + x2 = 0 + -218.75 Combine like terms: 218.75 + -218.75 = 0.00 0.00 + -33.75x + x2 = 0 + -218.75 -33.75x + x2 = 0 + -218.75 Combine like terms: 0 + -218.75 = -218.75 -33.75x + x2 = -218.75 The x term is -33.75x. Take half its coefficient (-16.875). Square it (284.765625) and add it to both sides. Add '284.765625' to each side of the equation. -33.75x + 284.765625 + x2 = -218.75 + 284.765625 Reorder the terms: 284.765625 + -33.75x + x2 = -218.75 + 284.765625 Combine like terms: -218.75 + 284.765625 = 66.015625 284.765625 + -33.75x + x2 = 66.015625 Factor a perfect square on the left side: (x + -16.875)(x + -16.875) = 66.015625 Calculate the square root of the right side: 8.125 Break this problem into two subproblems by setting (x + -16.875) equal to 8.125 and -8.125.Subproblem 1
x + -16.875 = 8.125 Simplifying x + -16.875 = 8.125 Reorder the terms: -16.875 + x = 8.125 Solving -16.875 + x = 8.125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.875' to each side of the equation. -16.875 + 16.875 + x = 8.125 + 16.875 Combine like terms: -16.875 + 16.875 = 0.000 0.000 + x = 8.125 + 16.875 x = 8.125 + 16.875 Combine like terms: 8.125 + 16.875 = 25 x = 25 Simplifying x = 25Subproblem 2
x + -16.875 = -8.125 Simplifying x + -16.875 = -8.125 Reorder the terms: -16.875 + x = -8.125 Solving -16.875 + x = -8.125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.875' to each side of the equation. -16.875 + 16.875 + x = -8.125 + 16.875 Combine like terms: -16.875 + 16.875 = 0.000 0.000 + x = -8.125 + 16.875 x = -8.125 + 16.875 Combine like terms: -8.125 + 16.875 = 8.75 x = 8.75 Simplifying x = 8.75Solution
The solution to the problem is based on the solutions from the subproblems. x = {25, 8.75}
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