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Simplifying x2 + -6x2 + 16x + -6 = 0 Reorder the terms: -6 + 16x + x2 + -6x2 = 0 Combine like terms: x2 + -6x2 = -5x2 -6 + 16x + -5x2 = 0 Solving -6 + 16x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 1.2 + -3.2x + x2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + -3.2x + -1.2 + x2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + -3.2x + x2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + -3.2x + x2 = 0 + -1.2 -3.2x + x2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 -3.2x + x2 = -1.2 The x term is -3.2x. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2x + 2.56 + x2 = -1.2 + 2.56 Reorder the terms: 2.56 + -3.2x + x2 = -1.2 + 2.56 Combine like terms: -1.2 + 2.56 = 1.36 2.56 + -3.2x + x2 = 1.36 Factor a perfect square on the left side: (x + -1.6)(x + -1.6) = 1.36 Calculate the square root of the right side: 1.166190379 Break this problem into two subproblems by setting (x + -1.6) equal to 1.166190379 and -1.166190379.Subproblem 1
x + -1.6 = 1.166190379 Simplifying x + -1.6 = 1.166190379 Reorder the terms: -1.6 + x = 1.166190379 Solving -1.6 + x = 1.166190379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = 1.166190379 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 1.166190379 + 1.6 x = 1.166190379 + 1.6 Combine like terms: 1.166190379 + 1.6 = 2.766190379 x = 2.766190379 Simplifying x = 2.766190379Subproblem 2
x + -1.6 = -1.166190379 Simplifying x + -1.6 = -1.166190379 Reorder the terms: -1.6 + x = -1.166190379 Solving -1.6 + x = -1.166190379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = -1.166190379 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -1.166190379 + 1.6 x = -1.166190379 + 1.6 Combine like terms: -1.166190379 + 1.6 = 0.433809621 x = 0.433809621 Simplifying x = 0.433809621Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.766190379, 0.433809621}
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