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Simplifying 10000 + -700x = 10x2 Solving 10000 + -700x = 10x2 Solving for variable 'x'. Combine like terms: 10x2 + -10x2 = 0 10000 + -700x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(1000 + -70x + -1x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(1000 + -70x + -1x2)' equal to zero and attempt to solve: Simplifying 1000 + -70x + -1x2 = 0 Solving 1000 + -70x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1000 + 70x + x2 = 0 Move the constant term to the right: Add '1000' to each side of the equation. -1000 + 70x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + 70x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + 70x + x2 = 0 + 1000 70x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 70x + x2 = 1000 The x term is 70x. Take half its coefficient (35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. 70x + 1225 + x2 = 1000 + 1225 Reorder the terms: 1225 + 70x + x2 = 1000 + 1225 Combine like terms: 1000 + 1225 = 2225 1225 + 70x + x2 = 2225 Factor a perfect square on the left side: (x + 35)(x + 35) = 2225 Calculate the square root of the right side: 47.16990566 Break this problem into two subproblems by setting (x + 35) equal to 47.16990566 and -47.16990566.Subproblem 1
x + 35 = 47.16990566 Simplifying x + 35 = 47.16990566 Reorder the terms: 35 + x = 47.16990566 Solving 35 + x = 47.16990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + x = 47.16990566 + -35 Combine like terms: 35 + -35 = 0 0 + x = 47.16990566 + -35 x = 47.16990566 + -35 Combine like terms: 47.16990566 + -35 = 12.16990566 x = 12.16990566 Simplifying x = 12.16990566Subproblem 2
x + 35 = -47.16990566 Simplifying x + 35 = -47.16990566 Reorder the terms: 35 + x = -47.16990566 Solving 35 + x = -47.16990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + x = -47.16990566 + -35 Combine like terms: 35 + -35 = 0 0 + x = -47.16990566 + -35 x = -47.16990566 + -35 Combine like terms: -47.16990566 + -35 = -82.16990566 x = -82.16990566 Simplifying x = -82.16990566Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.16990566, -82.16990566}Solution
x = {12.16990566, -82.16990566}
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