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Simplifying 80 + -1(10 + -2x)(8 + -2x) = 37.75 Multiply (10 + -2x) * (8 + -2x) 80 + -1(10(8 + -2x) + -2x * (8 + -2x)) = 37.75 80 + -1((8 * 10 + -2x * 10) + -2x * (8 + -2x)) = 37.75 80 + -1((80 + -20x) + -2x * (8 + -2x)) = 37.75 80 + -1(80 + -20x + (8 * -2x + -2x * -2x)) = 37.75 80 + -1(80 + -20x + (-16x + 4x2)) = 37.75 Combine like terms: -20x + -16x = -36x 80 + -1(80 + -36x + 4x2) = 37.75 80 + (80 * -1 + -36x * -1 + 4x2 * -1) = 37.75 80 + (-80 + 36x + -4x2) = 37.75 Combine like terms: 80 + -80 = 0 0 + 36x + -4x2 = 37.75 36x + -4x2 = 37.75 Solving 36x + -4x2 = 37.75 Solving for variable 'x'. Reorder the terms: -37.75 + 36x + -4x2 = 37.75 + -37.75 Combine like terms: 37.75 + -37.75 = 0.00 -37.75 + 36x + -4x2 = 0.00 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 9.4375 + -9x + x2 = 0.00 Move the constant term to the right: Add '-9.4375' to each side of the equation. 9.4375 + -9x + -9.4375 + x2 = 0.00 + -9.4375 Reorder the terms: 9.4375 + -9.4375 + -9x + x2 = 0.00 + -9.4375 Combine like terms: 9.4375 + -9.4375 = 0.0000 0.0000 + -9x + x2 = 0.00 + -9.4375 -9x + x2 = 0.00 + -9.4375 Combine like terms: 0.00 + -9.4375 = -9.4375 -9x + x2 = -9.4375 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 = -9.4375 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -9.4375 + 20.25 Combine like terms: -9.4375 + 20.25 = 10.8125 20.25 + -9x + x2 = 10.8125 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 10.8125 Calculate the square root of the right side: 3.288236609 Break this problem into two subproblems by setting (x + -4.5) equal to 3.288236609 and -3.288236609.Subproblem 1
x + -4.5 = 3.288236609 Simplifying x + -4.5 = 3.288236609 Reorder the terms: -4.5 + x = 3.288236609 Solving -4.5 + x = 3.288236609 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 = 3.288236609 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 3.288236609 + 4.5 x = 3.288236609 + 4.5 Combine like terms: 3.288236609 + 4.5 = 7.788236609 x = 7.788236609 Simplifying x = 7.788236609Subproblem 2
x + -4.5 = -3.288236609 Simplifying x + -4.5 = -3.288236609 Reorder the terms: -4.5 + x = -3.288236609 Solving -4.5 + x = -3.288236609 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 = -3.288236609 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -3.288236609 + 4.5 x = -3.288236609 + 4.5 Combine like terms: -3.288236609 + 4.5 = 1.211763391 x = 1.211763391 Simplifying x = 1.211763391Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.788236609, 1.211763391}
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