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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'. Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 16x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + 16x + 5x2)' equal to zero and attempt to solve: Simplifying 6 + 16x + 5x2 = 0 Solving 6 + 16x + 5x2 = 0 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 = -0.433809621 x = -0.433809621 Simplifying x = -0.433809621Subproblem 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 = -2.766190379 x = -2.766190379 Simplifying x = -2.766190379Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.433809621, -2.766190379}Solution
x = {-0.433809621, -2.766190379}
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