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Simplifying 80 + -1(8 + -2x)(10 + -2x) = 38.75 Multiply (8 + -2x) * (10 + -2x) 80 + -1(8(10 + -2x) + -2x * (10 + -2x)) = 38.75 80 + -1((10 * 8 + -2x * 8) + -2x * (10 + -2x)) = 38.75 80 + -1((80 + -16x) + -2x * (10 + -2x)) = 38.75 80 + -1(80 + -16x + (10 * -2x + -2x * -2x)) = 38.75 80 + -1(80 + -16x + (-20x + 4x2)) = 38.75 Combine like terms: -16x + -20x = -36x 80 + -1(80 + -36x + 4x2) = 38.75 80 + (80 * -1 + -36x * -1 + 4x2 * -1) = 38.75 80 + (-80 + 36x + -4x2) = 38.75 Combine like terms: 80 + -80 = 0 0 + 36x + -4x2 = 38.75 36x + -4x2 = 38.75 Solving 36x + -4x2 = 38.75 Solving for variable 'x'. Reorder the terms: -38.75 + 36x + -4x2 = 38.75 + -38.75 Combine like terms: 38.75 + -38.75 = 0.00 -38.75 + 36x + -4x2 = 0.00 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 9.6875 + -9x + x2 = 0.00 Move the constant term to the right: Add '-9.6875' to each side of the equation. 9.6875 + -9x + -9.6875 + x2 = 0.00 + -9.6875 Reorder the terms: 9.6875 + -9.6875 + -9x + x2 = 0.00 + -9.6875 Combine like terms: 9.6875 + -9.6875 = 0.0000 0.0000 + -9x + x2 = 0.00 + -9.6875 -9x + x2 = 0.00 + -9.6875 Combine like terms: 0.00 + -9.6875 = -9.6875 -9x + x2 = -9.6875 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -9.6875 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -9.6875 + 20.25 Combine like terms: -9.6875 + 20.25 = 10.5625 20.25 + -9x + x2 = 10.5625 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 10.5625 Calculate the square root of the right side: 3.25 Break this problem into two subproblems by setting (x + -4.5) equal to 3.25 and -3.25.Subproblem 1
x + -4.5 = 3.25 Simplifying x + -4.5 = 3.25 Reorder the terms: -4.5 + x = 3.25 Solving -4.5 + x = 3.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 3.25 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 3.25 + 4.5 x = 3.25 + 4.5 Combine like terms: 3.25 + 4.5 = 7.75 x = 7.75 Simplifying x = 7.75Subproblem 2
x + -4.5 = -3.25 Simplifying x + -4.5 = -3.25 Reorder the terms: -4.5 + x = -3.25 Solving -4.5 + x = -3.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -3.25 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -3.25 + 4.5 x = -3.25 + 4.5 Combine like terms: -3.25 + 4.5 = 1.25 x = 1.25 Simplifying x = 1.25Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.75, 1.25}
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