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Simplifying 2094x2 + 5940x + 5947 = 99000 Reorder the terms: 5947 + 5940x + 2094x2 = 99000 Solving 5947 + 5940x + 2094x2 = 99000 Solving for variable 'x'. Reorder the terms: 5947 + -99000 + 5940x + 2094x2 = 99000 + -99000 Combine like terms: 5947 + -99000 = -93053 -93053 + 5940x + 2094x2 = 99000 + -99000 Combine like terms: 99000 + -99000 = 0 -93053 + 5940x + 2094x2 = 0 Begin completing the square. Divide all terms by 2094 the coefficient of the squared term: Divide each side by '2094'. -44.43791786 + 2.836676218x + x2 = 0 Move the constant term to the right: Add '44.43791786' to each side of the equation. -44.43791786 + 2.836676218x + 44.43791786 + x2 = 0 + 44.43791786 Reorder the terms: -44.43791786 + 44.43791786 + 2.836676218x + x2 = 0 + 44.43791786 Combine like terms: -44.43791786 + 44.43791786 = 0.00000000 0.00000000 + 2.836676218x + x2 = 0 + 44.43791786 2.836676218x + x2 = 0 + 44.43791786 Combine like terms: 0 + 44.43791786 = 44.43791786 2.836676218x + x2 = 44.43791786 The x term is 2.836676218x. Take half its coefficient (1.418338109). Square it (2.011682991) and add it to both sides. Add '2.011682991' to each side of the equation. 2.836676218x + 2.011682991 + x2 = 44.43791786 + 2.011682991 Reorder the terms: 2.011682991 + 2.836676218x + x2 = 44.43791786 + 2.011682991 Combine like terms: 44.43791786 + 2.011682991 = 46.449600851 2.011682991 + 2.836676218x + x2 = 46.449600851 Factor a perfect square on the left side: (x + 1.418338109)(x + 1.418338109) = 46.449600851 Calculate the square root of the right side: 6.815394402 Break this problem into two subproblems by setting (x + 1.418338109) equal to 6.815394402 and -6.815394402.Subproblem 1
x + 1.418338109 = 6.815394402 Simplifying x + 1.418338109 = 6.815394402 Reorder the terms: 1.418338109 + x = 6.815394402 Solving 1.418338109 + x = 6.815394402 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.418338109' to each side of the equation. 1.418338109 + -1.418338109 + x = 6.815394402 + -1.418338109 Combine like terms: 1.418338109 + -1.418338109 = 0.000000000 0.000000000 + x = 6.815394402 + -1.418338109 x = 6.815394402 + -1.418338109 Combine like terms: 6.815394402 + -1.418338109 = 5.397056293 x = 5.397056293 Simplifying x = 5.397056293Subproblem 2
x + 1.418338109 = -6.815394402 Simplifying x + 1.418338109 = -6.815394402 Reorder the terms: 1.418338109 + x = -6.815394402 Solving 1.418338109 + x = -6.815394402 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.418338109' to each side of the equation. 1.418338109 + -1.418338109 + x = -6.815394402 + -1.418338109 Combine like terms: 1.418338109 + -1.418338109 = 0.000000000 0.000000000 + x = -6.815394402 + -1.418338109 x = -6.815394402 + -1.418338109 Combine like terms: -6.815394402 + -1.418338109 = -8.233732511 x = -8.233732511 Simplifying x = -8.233732511Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.397056293, -8.233732511}
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