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Simplifying -1(x2) + -100x + 375 = 0 Reorder the terms: 375 + -100x + -1x2 = 0 Solving 375 + -100x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -375 + 100x + x2 = 0 Move the constant term to the right: Add '375' to each side of the equation. -375 + 100x + 375 + x2 = 0 + 375 Reorder the terms: -375 + 375 + 100x + x2 = 0 + 375 Combine like terms: -375 + 375 = 0 0 + 100x + x2 = 0 + 375 100x + x2 = 0 + 375 Combine like terms: 0 + 375 = 375 100x + x2 = 375 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 = 375 + 2500 Reorder the terms: 2500 + 100x + x2 = 375 + 2500 Combine like terms: 375 + 2500 = 2875 2500 + 100x + x2 = 2875 Factor a perfect square on the left side: (x + 50)(x + 50) = 2875 Calculate the square root of the right side: 53.619026474 Break this problem into two subproblems by setting (x + 50) equal to 53.619026474 and -53.619026474.Subproblem 1
x + 50 = 53.619026474 Simplifying x + 50 = 53.619026474 Reorder the terms: 50 + x = 53.619026474 Solving 50 + x = 53.619026474 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 = 53.619026474 + -50 Combine like terms: 50 + -50 = 0 0 + x = 53.619026474 + -50 x = 53.619026474 + -50 Combine like terms: 53.619026474 + -50 = 3.619026474 x = 3.619026474 Simplifying x = 3.619026474Subproblem 2
x + 50 = -53.619026474 Simplifying x + 50 = -53.619026474 Reorder the terms: 50 + x = -53.619026474 Solving 50 + x = -53.619026474 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 = -53.619026474 + -50 Combine like terms: 50 + -50 = 0 0 + x = -53.619026474 + -50 x = -53.619026474 + -50 Combine like terms: -53.619026474 + -50 = -103.619026474 x = -103.619026474 Simplifying x = -103.619026474Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.619026474, -103.619026474}
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