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Simplifying 10x2 = 27x + -16 Reorder the terms: 10x2 = -16 + 27x Solving 10x2 = -16 + 27x Solving for variable 'x'. Reorder the terms: 16 + -27x + 10x2 = -16 + 27x + 16 + -27x Reorder the terms: 16 + -27x + 10x2 = -16 + 16 + 27x + -27x Combine like terms: -16 + 16 = 0 16 + -27x + 10x2 = 0 + 27x + -27x 16 + -27x + 10x2 = 27x + -27x Combine like terms: 27x + -27x = 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 = 1.821699057 x = 1.821699057 Simplifying x = 1.821699057Subproblem 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 = 0.878300943 x = 0.878300943 Simplifying x = 0.878300943Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.821699057, 0.878300943}
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