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Simplifying 4(x2 + 75x + -250) = 0 Reorder the terms: 4(-250 + 75x + x2) = 0 (-250 * 4 + 75x * 4 + x2 * 4) = 0 (-1000 + 300x + 4x2) = 0 Solving -1000 + 300x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-250 + 75x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-250 + 75x + x2)' equal to zero and attempt to solve: Simplifying -250 + 75x + x2 = 0 Solving -250 + 75x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '250' to each side of the equation. -250 + 75x + 250 + x2 = 0 + 250 Reorder the terms: -250 + 250 + 75x + x2 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + 75x + x2 = 0 + 250 75x + x2 = 0 + 250 Combine like terms: 0 + 250 = 250 75x + x2 = 250 The x term is 75x. Take half its coefficient (37.5). Square it (1406.25) and add it to both sides. Add '1406.25' to each side of the equation. 75x + 1406.25 + x2 = 250 + 1406.25 Reorder the terms: 1406.25 + 75x + x2 = 250 + 1406.25 Combine like terms: 250 + 1406.25 = 1656.25 1406.25 + 75x + x2 = 1656.25 Factor a perfect square on the left side: (x + 37.5)(x + 37.5) = 1656.25 Calculate the square root of the right side: 40.69705149 Break this problem into two subproblems by setting (x + 37.5) equal to 40.69705149 and -40.69705149.Subproblem 1
x + 37.5 = 40.69705149 Simplifying x + 37.5 = 40.69705149 Reorder the terms: 37.5 + x = 40.69705149 Solving 37.5 + x = 40.69705149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-37.5' to each side of the equation. 37.5 + -37.5 + x = 40.69705149 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + x = 40.69705149 + -37.5 x = 40.69705149 + -37.5 Combine like terms: 40.69705149 + -37.5 = 3.19705149 x = 3.19705149 Simplifying x = 3.19705149Subproblem 2
x + 37.5 = -40.69705149 Simplifying x + 37.5 = -40.69705149 Reorder the terms: 37.5 + x = -40.69705149 Solving 37.5 + x = -40.69705149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-37.5' to each side of the equation. 37.5 + -37.5 + x = -40.69705149 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + x = -40.69705149 + -37.5 x = -40.69705149 + -37.5 Combine like terms: -40.69705149 + -37.5 = -78.19705149 x = -78.19705149 Simplifying x = -78.19705149Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.19705149, -78.19705149}Solution
x = {3.19705149, -78.19705149}
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