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Simplifying 4x2 + -120x = 1000 Reorder the terms: -120x + 4x2 = 1000 Solving -120x + 4x2 = 1000 Solving for variable 'x'. Reorder the terms: -1000 + -120x + 4x2 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 -1000 + -120x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-250 + -30x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-250 + -30x + x2)' equal to zero and attempt to solve: Simplifying -250 + -30x + x2 = 0 Solving -250 + -30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '250' to each side of the equation. -250 + -30x + 250 + x2 = 0 + 250 Reorder the terms: -250 + 250 + -30x + x2 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + -30x + x2 = 0 + 250 -30x + x2 = 0 + 250 Combine like terms: 0 + 250 = 250 -30x + x2 = 250 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = 250 + 225 Reorder the terms: 225 + -30x + x2 = 250 + 225 Combine like terms: 250 + 225 = 475 225 + -30x + x2 = 475 Factor a perfect square on the left side: (x + -15)(x + -15) = 475 Calculate the square root of the right side: 21.794494718 Break this problem into two subproblems by setting (x + -15) equal to 21.794494718 and -21.794494718.Subproblem 1
x + -15 = 21.794494718 Simplifying x + -15 = 21.794494718 Reorder the terms: -15 + x = 21.794494718 Solving -15 + x = 21.794494718 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 21.794494718 + 15 Combine like terms: -15 + 15 = 0 0 + x = 21.794494718 + 15 x = 21.794494718 + 15 Combine like terms: 21.794494718 + 15 = 36.794494718 x = 36.794494718 Simplifying x = 36.794494718Subproblem 2
x + -15 = -21.794494718 Simplifying x + -15 = -21.794494718 Reorder the terms: -15 + x = -21.794494718 Solving -15 + x = -21.794494718 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -21.794494718 + 15 Combine like terms: -15 + 15 = 0 0 + x = -21.794494718 + 15 x = -21.794494718 + 15 Combine like terms: -21.794494718 + 15 = -6.794494718 x = -6.794494718 Simplifying x = -6.794494718Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.794494718, -6.794494718}Solution
x = {36.794494718, -6.794494718}
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