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Simplifying -2.7x2 + 35x + 3 = 0 Reorder the terms: 3 + 35x + -2.7x2 = 0 Solving 3 + 35x + -2.7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2.7 the coefficient of the squared term: Divide each side by '-2.7'. -1.111111111 + -12.96296296x + x2 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + -12.96296296x + 1.111111111 + x2 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + -12.96296296x + x2 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + -12.96296296x + x2 = 0 + 1.111111111 -12.96296296x + x2 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 -12.96296296x + x2 = 1.111111111 The x term is -12.96296296x. Take half its coefficient (-6.48148148). Square it (42.00960218) and add it to both sides. Add '42.00960218' to each side of the equation. -12.96296296x + 42.00960218 + x2 = 1.111111111 + 42.00960218 Reorder the terms: 42.00960218 + -12.96296296x + x2 = 1.111111111 + 42.00960218 Combine like terms: 1.111111111 + 42.00960218 = 43.120713291 42.00960218 + -12.96296296x + x2 = 43.120713291 Factor a perfect square on the left side: (x + -6.48148148)(x + -6.48148148) = 43.120713291 Calculate the square root of the right side: 6.566636376 Break this problem into two subproblems by setting (x + -6.48148148) equal to 6.566636376 and -6.566636376.Subproblem 1
x + -6.48148148 = 6.566636376 Simplifying x + -6.48148148 = 6.566636376 Reorder the terms: -6.48148148 + x = 6.566636376 Solving -6.48148148 + x = 6.566636376 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.48148148' to each side of the equation. -6.48148148 + 6.48148148 + x = 6.566636376 + 6.48148148 Combine like terms: -6.48148148 + 6.48148148 = 0.00000000 0.00000000 + x = 6.566636376 + 6.48148148 x = 6.566636376 + 6.48148148 Combine like terms: 6.566636376 + 6.48148148 = 13.048117856 x = 13.048117856 Simplifying x = 13.048117856Subproblem 2
x + -6.48148148 = -6.566636376 Simplifying x + -6.48148148 = -6.566636376 Reorder the terms: -6.48148148 + x = -6.566636376 Solving -6.48148148 + x = -6.566636376 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.48148148' to each side of the equation. -6.48148148 + 6.48148148 + x = -6.566636376 + 6.48148148 Combine like terms: -6.48148148 + 6.48148148 = 0.00000000 0.00000000 + x = -6.566636376 + 6.48148148 x = -6.566636376 + 6.48148148 Combine like terms: -6.566636376 + 6.48148148 = -0.085154896 x = -0.085154896 Simplifying x = -0.085154896Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.048117856, -0.085154896}
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