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Simplifying x2 + -4 + -95x = 0 Reorder the terms: -4 + -95x + x2 = 0 Solving -4 + -95x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -95x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -95x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -95x + x2 = 0 + 4 -95x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -95x + x2 = 4 The x term is -95x. Take half its coefficient (-47.5). Square it (2256.25) and add it to both sides. Add '2256.25' to each side of the equation. -95x + 2256.25 + x2 = 4 + 2256.25 Reorder the terms: 2256.25 + -95x + x2 = 4 + 2256.25 Combine like terms: 4 + 2256.25 = 2260.25 2256.25 + -95x + x2 = 2260.25 Factor a perfect square on the left side: (x + -47.5)(x + -47.5) = 2260.25 Calculate the square root of the right side: 47.542086618 Break this problem into two subproblems by setting (x + -47.5) equal to 47.542086618 and -47.542086618.Subproblem 1
x + -47.5 = 47.542086618 Simplifying x + -47.5 = 47.542086618 Reorder the terms: -47.5 + x = 47.542086618 Solving -47.5 + x = 47.542086618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '47.5' to each side of the equation. -47.5 + 47.5 + x = 47.542086618 + 47.5 Combine like terms: -47.5 + 47.5 = 0.0 0.0 + x = 47.542086618 + 47.5 x = 47.542086618 + 47.5 Combine like terms: 47.542086618 + 47.5 = 95.042086618 x = 95.042086618 Simplifying x = 95.042086618Subproblem 2
x + -47.5 = -47.542086618 Simplifying x + -47.5 = -47.542086618 Reorder the terms: -47.5 + x = -47.542086618 Solving -47.5 + x = -47.542086618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '47.5' to each side of the equation. -47.5 + 47.5 + x = -47.542086618 + 47.5 Combine like terms: -47.5 + 47.5 = 0.0 0.0 + x = -47.542086618 + 47.5 x = -47.542086618 + 47.5 Combine like terms: -47.542086618 + 47.5 = -0.042086618 x = -0.042086618 Simplifying x = -0.042086618Solution
The solution to the problem is based on the solutions from the subproblems. x = {95.042086618, -0.042086618}
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