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Simplifying (10x + -27) * 1.1x = 200 Reorder the terms: (-27 + 10x) * 1.1x = 200 Reorder the terms for easier multiplication: 1.1x(-27 + 10x) = 200 (-27 * 1.1x + 10x * 1.1x) = 200 (-29.7x + 11x2) = 200 Solving -29.7x + 11x2 = 200 Solving for variable 'x'. Reorder the terms: -200 + -29.7x + 11x2 = 200 + -200 Combine like terms: 200 + -200 = 0 -200 + -29.7x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -18.18181818 + -2.7x + x2 = 0 Move the constant term to the right: Add '18.18181818' to each side of the equation. -18.18181818 + -2.7x + 18.18181818 + x2 = 0 + 18.18181818 Reorder the terms: -18.18181818 + 18.18181818 + -2.7x + x2 = 0 + 18.18181818 Combine like terms: -18.18181818 + 18.18181818 = 0.00000000 0.00000000 + -2.7x + x2 = 0 + 18.18181818 -2.7x + x2 = 0 + 18.18181818 Combine like terms: 0 + 18.18181818 = 18.18181818 -2.7x + x2 = 18.18181818 The x term is -2.7x. Take half its coefficient (-1.35). Square it (1.8225) and add it to both sides. Add '1.8225' to each side of the equation. -2.7x + 1.8225 + x2 = 18.18181818 + 1.8225 Reorder the terms: 1.8225 + -2.7x + x2 = 18.18181818 + 1.8225 Combine like terms: 18.18181818 + 1.8225 = 20.00431818 1.8225 + -2.7x + x2 = 20.00431818 Factor a perfect square on the left side: (x + -1.35)(x + -1.35) = 20.00431818 Calculate the square root of the right side: 4.472618716 Break this problem into two subproblems by setting (x + -1.35) equal to 4.472618716 and -4.472618716.Subproblem 1
x + -1.35 = 4.472618716 Simplifying x + -1.35 = 4.472618716 Reorder the terms: -1.35 + x = 4.472618716 Solving -1.35 + x = 4.472618716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.35' to each side of the equation. -1.35 + 1.35 + x = 4.472618716 + 1.35 Combine like terms: -1.35 + 1.35 = 0.00 0.00 + x = 4.472618716 + 1.35 x = 4.472618716 + 1.35 Combine like terms: 4.472618716 + 1.35 = 5.822618716 x = 5.822618716 Simplifying x = 5.822618716Subproblem 2
x + -1.35 = -4.472618716 Simplifying x + -1.35 = -4.472618716 Reorder the terms: -1.35 + x = -4.472618716 Solving -1.35 + x = -4.472618716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.35' to each side of the equation. -1.35 + 1.35 + x = -4.472618716 + 1.35 Combine like terms: -1.35 + 1.35 = 0.00 0.00 + x = -4.472618716 + 1.35 x = -4.472618716 + 1.35 Combine like terms: -4.472618716 + 1.35 = -3.122618716 x = -3.122618716 Simplifying x = -3.122618716Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.822618716, -3.122618716}
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