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Simplifying -0.05X2 + 70X + -6000 = 0 Reorder the terms: -6000 + 70X + -0.05X2 = 0 Solving -6000 + 70X + -0.05X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. 120000 + -1400X + X2 = 0 Move the constant term to the right: Add '-120000' to each side of the equation. 120000 + -1400X + -120000 + X2 = 0 + -120000 Reorder the terms: 120000 + -120000 + -1400X + X2 = 0 + -120000 Combine like terms: 120000 + -120000 = 0 0 + -1400X + X2 = 0 + -120000 -1400X + X2 = 0 + -120000 Combine like terms: 0 + -120000 = -120000 -1400X + X2 = -120000 The X term is -1400X. Take half its coefficient (-700). Square it (490000) and add it to both sides. Add '490000' to each side of the equation. -1400X + 490000 + X2 = -120000 + 490000 Reorder the terms: 490000 + -1400X + X2 = -120000 + 490000 Combine like terms: -120000 + 490000 = 370000 490000 + -1400X + X2 = 370000 Factor a perfect square on the left side: (X + -700)(X + -700) = 370000 Calculate the square root of the right side: 608.27625303 Break this problem into two subproblems by setting (X + -700) equal to 608.27625303 and -608.27625303.Subproblem 1
X + -700 = 608.27625303 Simplifying X + -700 = 608.27625303 Reorder the terms: -700 + X = 608.27625303 Solving -700 + X = 608.27625303 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '700' to each side of the equation. -700 + 700 + X = 608.27625303 + 700 Combine like terms: -700 + 700 = 0 0 + X = 608.27625303 + 700 X = 608.27625303 + 700 Combine like terms: 608.27625303 + 700 = 1308.27625303 X = 1308.27625303 Simplifying X = 1308.27625303Subproblem 2
X + -700 = -608.27625303 Simplifying X + -700 = -608.27625303 Reorder the terms: -700 + X = -608.27625303 Solving -700 + X = -608.27625303 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '700' to each side of the equation. -700 + 700 + X = -608.27625303 + 700 Combine like terms: -700 + 700 = 0 0 + X = -608.27625303 + 700 X = -608.27625303 + 700 Combine like terms: -608.27625303 + 700 = 91.72374697 X = 91.72374697 Simplifying X = 91.72374697Solution
The solution to the problem is based on the solutions from the subproblems. X = {1308.27625303, 91.72374697}
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