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Simplifying 25.32x2 + -3900x + -156 = 6.74 Reorder the terms: -156 + -3900x + 25.32x2 = 6.74 Solving -156 + -3900x + 25.32x2 = 6.74 Solving for variable 'x'. Reorder the terms: -156 + -6.74 + -3900x + 25.32x2 = 6.74 + -6.74 Combine like terms: -156 + -6.74 = -162.74 -162.74 + -3900x + 25.32x2 = 6.74 + -6.74 Combine like terms: 6.74 + -6.74 = 0.00 -162.74 + -3900x + 25.32x2 = 0.00 Begin completing the square. Divide all terms by 25.32 the coefficient of the squared term: Divide each side by '25.32'. -6.427330174 + -154.028436x + x2 = 0 Move the constant term to the right: Add '6.427330174' to each side of the equation. -6.427330174 + -154.028436x + 6.427330174 + x2 = 0 + 6.427330174 Reorder the terms: -6.427330174 + 6.427330174 + -154.028436x + x2 = 0 + 6.427330174 Combine like terms: -6.427330174 + 6.427330174 = 0.000000000 0.000000000 + -154.028436x + x2 = 0 + 6.427330174 -154.028436x + x2 = 0 + 6.427330174 Combine like terms: 0 + 6.427330174 = 6.427330174 -154.028436x + x2 = 6.427330174 The x term is -154.028436x. Take half its coefficient (-77.014218). Square it (5931.189774) and add it to both sides. Add '5931.189774' to each side of the equation. -154.028436x + 5931.189774 + x2 = 6.427330174 + 5931.189774 Reorder the terms: 5931.189774 + -154.028436x + x2 = 6.427330174 + 5931.189774 Combine like terms: 6.427330174 + 5931.189774 = 5937.617104174 5931.189774 + -154.028436x + x2 = 5937.617104174 Factor a perfect square on the left side: (x + -77.014218)(x + -77.014218) = 5937.617104174 Calculate the square root of the right side: 77.055934906 Break this problem into two subproblems by setting (x + -77.014218) equal to 77.055934906 and -77.055934906.Subproblem 1
x + -77.014218 = 77.055934906 Simplifying x + -77.014218 = 77.055934906 Reorder the terms: -77.014218 + x = 77.055934906 Solving -77.014218 + x = 77.055934906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '77.014218' to each side of the equation. -77.014218 + 77.014218 + x = 77.055934906 + 77.014218 Combine like terms: -77.014218 + 77.014218 = 0.000000 0.000000 + x = 77.055934906 + 77.014218 x = 77.055934906 + 77.014218 Combine like terms: 77.055934906 + 77.014218 = 154.070152906 x = 154.070152906 Simplifying x = 154.070152906Subproblem 2
x + -77.014218 = -77.055934906 Simplifying x + -77.014218 = -77.055934906 Reorder the terms: -77.014218 + x = -77.055934906 Solving -77.014218 + x = -77.055934906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '77.014218' to each side of the equation. -77.014218 + 77.014218 + x = -77.055934906 + 77.014218 Combine like terms: -77.014218 + 77.014218 = 0.000000 0.000000 + x = -77.055934906 + 77.014218 x = -77.055934906 + 77.014218 Combine like terms: -77.055934906 + 77.014218 = -0.041716906 x = -0.041716906 Simplifying x = -0.041716906Solution
The solution to the problem is based on the solutions from the subproblems. x = {154.070152906, -0.041716906}
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