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Simplifying 7x + 10x(200 + -1x) = 1625 7x + (200 * 10x + -1x * 10x) = 1625 7x + (2000x + -10x2) = 1625 Combine like terms: 7x + 2000x = 2007x 2007x + -10x2 = 1625 Solving 2007x + -10x2 = 1625 Solving for variable 'x'. Reorder the terms: -1625 + 2007x + -10x2 = 1625 + -1625 Combine like terms: 1625 + -1625 = 0 -1625 + 2007x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. 162.5 + -200.7x + x2 = 0.0 Move the constant term to the right: Add '-162.5' to each side of the equation. 162.5 + -200.7x + -162.5 + x2 = 0.0 + -162.5 Reorder the terms: 162.5 + -162.5 + -200.7x + x2 = 0.0 + -162.5 Combine like terms: 162.5 + -162.5 = 0.0 0.0 + -200.7x + x2 = 0.0 + -162.5 -200.7x + x2 = 0.0 + -162.5 Combine like terms: 0.0 + -162.5 = -162.5 -200.7x + x2 = -162.5 The x term is -200.7x. Take half its coefficient (-100.35). Square it (10070.1225) and add it to both sides. Add '10070.1225' to each side of the equation. -200.7x + 10070.1225 + x2 = -162.5 + 10070.1225 Reorder the terms: 10070.1225 + -200.7x + x2 = -162.5 + 10070.1225 Combine like terms: -162.5 + 10070.1225 = 9907.6225 10070.1225 + -200.7x + x2 = 9907.6225 Factor a perfect square on the left side: (x + -100.35)(x + -100.35) = 9907.6225 Calculate the square root of the right side: 99.537040844 Break this problem into two subproblems by setting (x + -100.35) equal to 99.537040844 and -99.537040844.Subproblem 1
x + -100.35 = 99.537040844 Simplifying x + -100.35 = 99.537040844 Reorder the terms: -100.35 + x = 99.537040844 Solving -100.35 + x = 99.537040844 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100.35' to each side of the equation. -100.35 + 100.35 + x = 99.537040844 + 100.35 Combine like terms: -100.35 + 100.35 = 0.00 0.00 + x = 99.537040844 + 100.35 x = 99.537040844 + 100.35 Combine like terms: 99.537040844 + 100.35 = 199.887040844 x = 199.887040844 Simplifying x = 199.887040844Subproblem 2
x + -100.35 = -99.537040844 Simplifying x + -100.35 = -99.537040844 Reorder the terms: -100.35 + x = -99.537040844 Solving -100.35 + x = -99.537040844 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100.35' to each side of the equation. -100.35 + 100.35 + x = -99.537040844 + 100.35 Combine like terms: -100.35 + 100.35 = 0.00 0.00 + x = -99.537040844 + 100.35 x = -99.537040844 + 100.35 Combine like terms: -99.537040844 + 100.35 = 0.812959156 x = 0.812959156 Simplifying x = 0.812959156Solution
The solution to the problem is based on the solutions from the subproblems. x = {199.887040844, 0.812959156}
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