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Simplifying 47x2 + 88x + 27 = 0 Reorder the terms: 27 + 88x + 47x2 = 0 Solving 27 + 88x + 47x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 47 the coefficient of the squared term: Divide each side by '47'. 0.5744680851 + 1.872340426x + x2 = 0 Move the constant term to the right: Add '-0.5744680851' to each side of the equation. 0.5744680851 + 1.872340426x + -0.5744680851 + x2 = 0 + -0.5744680851 Reorder the terms: 0.5744680851 + -0.5744680851 + 1.872340426x + x2 = 0 + -0.5744680851 Combine like terms: 0.5744680851 + -0.5744680851 = 0.0000000000 0.0000000000 + 1.872340426x + x2 = 0 + -0.5744680851 1.872340426x + x2 = 0 + -0.5744680851 Combine like terms: 0 + -0.5744680851 = -0.5744680851 1.872340426x + x2 = -0.5744680851 The x term is 1.872340426x. Take half its coefficient (0.936170213). Square it (0.8764146677) and add it to both sides. Add '0.8764146677' to each side of the equation. 1.872340426x + 0.8764146677 + x2 = -0.5744680851 + 0.8764146677 Reorder the terms: 0.8764146677 + 1.872340426x + x2 = -0.5744680851 + 0.8764146677 Combine like terms: -0.5744680851 + 0.8764146677 = 0.3019465826 0.8764146677 + 1.872340426x + x2 = 0.3019465826 Factor a perfect square on the left side: (x + 0.936170213)(x + 0.936170213) = 0.3019465826 Calculate the square root of the right side: 0.549496663 Break this problem into two subproblems by setting (x + 0.936170213) equal to 0.549496663 and -0.549496663.Subproblem 1
x + 0.936170213 = 0.549496663 Simplifying x + 0.936170213 = 0.549496663 Reorder the terms: 0.936170213 + x = 0.549496663 Solving 0.936170213 + x = 0.549496663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.936170213' to each side of the equation. 0.936170213 + -0.936170213 + x = 0.549496663 + -0.936170213 Combine like terms: 0.936170213 + -0.936170213 = 0.000000000 0.000000000 + x = 0.549496663 + -0.936170213 x = 0.549496663 + -0.936170213 Combine like terms: 0.549496663 + -0.936170213 = -0.38667355 x = -0.38667355 Simplifying x = -0.38667355Subproblem 2
x + 0.936170213 = -0.549496663 Simplifying x + 0.936170213 = -0.549496663 Reorder the terms: 0.936170213 + x = -0.549496663 Solving 0.936170213 + x = -0.549496663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.936170213' to each side of the equation. 0.936170213 + -0.936170213 + x = -0.549496663 + -0.936170213 Combine like terms: 0.936170213 + -0.936170213 = 0.000000000 0.000000000 + x = -0.549496663 + -0.936170213 x = -0.549496663 + -0.936170213 Combine like terms: -0.549496663 + -0.936170213 = -1.485666876 x = -1.485666876 Simplifying x = -1.485666876Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.38667355, -1.485666876}
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