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Simplifying -4.9x2 + 29.4x + -15.9 = 0 Reorder the terms: -15.9 + 29.4x + -4.9x2 = 0 Solving -15.9 + 29.4x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 3.244897959 + -6x + x2 = 0 Move the constant term to the right: Add '-3.244897959' to each side of the equation. 3.244897959 + -6x + -3.244897959 + x2 = 0 + -3.244897959 Reorder the terms: 3.244897959 + -3.244897959 + -6x + x2 = 0 + -3.244897959 Combine like terms: 3.244897959 + -3.244897959 = 0.000000000 0.000000000 + -6x + x2 = 0 + -3.244897959 -6x + x2 = 0 + -3.244897959 Combine like terms: 0 + -3.244897959 = -3.244897959 -6x + x2 = -3.244897959 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -3.244897959 + 9 Reorder the terms: 9 + -6x + x2 = -3.244897959 + 9 Combine like terms: -3.244897959 + 9 = 5.755102041 9 + -6x + x2 = 5.755102041 Factor a perfect square on the left side: (x + -3)(x + -3) = 5.755102041 Calculate the square root of the right side: 2.398979375 Break this problem into two subproblems by setting (x + -3) equal to 2.398979375 and -2.398979375.Subproblem 1
x + -3 = 2.398979375 Simplifying x + -3 = 2.398979375 Reorder the terms: -3 + x = 2.398979375 Solving -3 + x = 2.398979375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.398979375 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.398979375 + 3 x = 2.398979375 + 3 Combine like terms: 2.398979375 + 3 = 5.398979375 x = 5.398979375 Simplifying x = 5.398979375Subproblem 2
x + -3 = -2.398979375 Simplifying x + -3 = -2.398979375 Reorder the terms: -3 + x = -2.398979375 Solving -3 + x = -2.398979375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.398979375 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.398979375 + 3 x = -2.398979375 + 3 Combine like terms: -2.398979375 + 3 = 0.601020625 x = 0.601020625 Simplifying x = 0.601020625Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.398979375, 0.601020625}
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