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Simplifying 10x2 + 27x = -16 Reorder the terms: 27x + 10x2 = -16 Solving 27x + 10x2 = -16 Solving for variable 'x'. Reorder the terms: 16 + 27x + 10x2 = -16 + 16 Combine like terms: -16 + 16 = 0 16 + 27x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1.6 + 2.7x + x2 = 0 Move the constant term to the right: Add '-1.6' to each side of the equation. 1.6 + 2.7x + -1.6 + x2 = 0 + -1.6 Reorder the terms: 1.6 + -1.6 + 2.7x + x2 = 0 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + 2.7x + x2 = 0 + -1.6 2.7x + x2 = 0 + -1.6 Combine like terms: 0 + -1.6 = -1.6 2.7x + x2 = -1.6 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 = -1.6 + 1.8225 Reorder the terms: 1.8225 + 2.7x + x2 = -1.6 + 1.8225 Combine like terms: -1.6 + 1.8225 = 0.2225 1.8225 + 2.7x + x2 = 0.2225 Factor a perfect square on the left side: (x + 1.35)(x + 1.35) = 0.2225 Calculate the square root of the right side: 0.471699057 Break this problem into two subproblems by setting (x + 1.35) equal to 0.471699057 and -0.471699057.Subproblem 1
x + 1.35 = 0.471699057 Simplifying x + 1.35 = 0.471699057 Reorder the terms: 1.35 + x = 0.471699057 Solving 1.35 + x = 0.471699057 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 = 0.471699057 + -1.35 Combine like terms: 1.35 + -1.35 = 0.00 0.00 + x = 0.471699057 + -1.35 x = 0.471699057 + -1.35 Combine like terms: 0.471699057 + -1.35 = -0.878300943 x = -0.878300943 Simplifying x = -0.878300943Subproblem 2
x + 1.35 = -0.471699057 Simplifying x + 1.35 = -0.471699057 Reorder the terms: 1.35 + x = -0.471699057 Solving 1.35 + x = -0.471699057 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 = -0.471699057 + -1.35 Combine like terms: 1.35 + -1.35 = 0.00 0.00 + x = -0.471699057 + -1.35 x = -0.471699057 + -1.35 Combine like terms: -0.471699057 + -1.35 = -1.821699057 x = -1.821699057 Simplifying x = -1.821699057Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.878300943, -1.821699057}
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