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Simplifying 10x2 + -27x + -800 = 9.7 Reorder the terms: -800 + -27x + 10x2 = 9.7 Solving -800 + -27x + 10x2 = 9.7 Solving for variable 'x'. Reorder the terms: -800 + -9.7 + -27x + 10x2 = 9.7 + -9.7 Combine like terms: -800 + -9.7 = -809.7 -809.7 + -27x + 10x2 = 9.7 + -9.7 Combine like terms: 9.7 + -9.7 = 0.0 -809.7 + -27x + 10x2 = 0.0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -80.97 + -2.7x + x2 = 0.0 Move the constant term to the right: Add '80.97' to each side of the equation. -80.97 + -2.7x + 80.97 + x2 = 0.0 + 80.97 Reorder the terms: -80.97 + 80.97 + -2.7x + x2 = 0.0 + 80.97 Combine like terms: -80.97 + 80.97 = 0.00 0.00 + -2.7x + x2 = 0.0 + 80.97 -2.7x + x2 = 0.0 + 80.97 Combine like terms: 0.0 + 80.97 = 80.97 -2.7x + x2 = 80.97 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 = 80.97 + 1.8225 Reorder the terms: 1.8225 + -2.7x + x2 = 80.97 + 1.8225 Combine like terms: 80.97 + 1.8225 = 82.7925 1.8225 + -2.7x + x2 = 82.7925 Factor a perfect square on the left side: (x + -1.35)(x + -1.35) = 82.7925 Calculate the square root of the right side: 9.099038411 Break this problem into two subproblems by setting (x + -1.35) equal to 9.099038411 and -9.099038411.Subproblem 1
x + -1.35 = 9.099038411 Simplifying x + -1.35 = 9.099038411 Reorder the terms: -1.35 + x = 9.099038411 Solving -1.35 + x = 9.099038411 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 = 9.099038411 + 1.35 Combine like terms: -1.35 + 1.35 = 0.00 0.00 + x = 9.099038411 + 1.35 x = 9.099038411 + 1.35 Combine like terms: 9.099038411 + 1.35 = 10.449038411 x = 10.449038411 Simplifying x = 10.449038411Subproblem 2
x + -1.35 = -9.099038411 Simplifying x + -1.35 = -9.099038411 Reorder the terms: -1.35 + x = -9.099038411 Solving -1.35 + x = -9.099038411 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 = -9.099038411 + 1.35 Combine like terms: -1.35 + 1.35 = 0.00 0.00 + x = -9.099038411 + 1.35 x = -9.099038411 + 1.35 Combine like terms: -9.099038411 + 1.35 = -7.749038411 x = -7.749038411 Simplifying x = -7.749038411Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.449038411, -7.749038411}
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