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Simplifying 2x2 + 200x + -3150 = 0 Reorder the terms: -3150 + 200x + 2x2 = 0 Solving -3150 + 200x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1575 + 100x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1575 + 100x + x2)' equal to zero and attempt to solve: Simplifying -1575 + 100x + x2 = 0 Solving -1575 + 100x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1575' to each side of the equation. -1575 + 100x + 1575 + x2 = 0 + 1575 Reorder the terms: -1575 + 1575 + 100x + x2 = 0 + 1575 Combine like terms: -1575 + 1575 = 0 0 + 100x + x2 = 0 + 1575 100x + x2 = 0 + 1575 Combine like terms: 0 + 1575 = 1575 100x + x2 = 1575 The x term is 100x. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100x + 2500 + x2 = 1575 + 2500 Reorder the terms: 2500 + 100x + x2 = 1575 + 2500 Combine like terms: 1575 + 2500 = 4075 2500 + 100x + x2 = 4075 Factor a perfect square on the left side: (x + 50)(x + 50) = 4075 Calculate the square root of the right side: 63.835726674 Break this problem into two subproblems by setting (x + 50) equal to 63.835726674 and -63.835726674.Subproblem 1
x + 50 = 63.835726674 Simplifying x + 50 = 63.835726674 Reorder the terms: 50 + x = 63.835726674 Solving 50 + x = 63.835726674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = 63.835726674 + -50 Combine like terms: 50 + -50 = 0 0 + x = 63.835726674 + -50 x = 63.835726674 + -50 Combine like terms: 63.835726674 + -50 = 13.835726674 x = 13.835726674 Simplifying x = 13.835726674Subproblem 2
x + 50 = -63.835726674 Simplifying x + 50 = -63.835726674 Reorder the terms: 50 + x = -63.835726674 Solving 50 + x = -63.835726674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = -63.835726674 + -50 Combine like terms: 50 + -50 = 0 0 + x = -63.835726674 + -50 x = -63.835726674 + -50 Combine like terms: -63.835726674 + -50 = -113.835726674 x = -113.835726674 Simplifying x = -113.835726674Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.835726674, -113.835726674}Solution
x = {13.835726674, -113.835726674}
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