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Simplifying 4x2 + -12x = 1000 Reorder the terms: -12x + 4x2 = 1000 Solving -12x + 4x2 = 1000 Solving for variable 'x'. Reorder the terms: -1000 + -12x + 4x2 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 -1000 + -12x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-250 + -3x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-250 + -3x + x2)' equal to zero and attempt to solve: Simplifying -250 + -3x + x2 = 0 Solving -250 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '250' to each side of the equation. -250 + -3x + 250 + x2 = 0 + 250 Reorder the terms: -250 + 250 + -3x + x2 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + -3x + x2 = 0 + 250 -3x + x2 = 0 + 250 Combine like terms: 0 + 250 = 250 -3x + x2 = 250 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 250 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 250 + 2.25 Combine like terms: 250 + 2.25 = 252.25 2.25 + -3x + x2 = 252.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 252.25 Calculate the square root of the right side: 15.882380174 Break this problem into two subproblems by setting (x + -1.5) equal to 15.882380174 and -15.882380174.Subproblem 1
x + -1.5 = 15.882380174 Simplifying x + -1.5 = 15.882380174 Reorder the terms: -1.5 + x = 15.882380174 Solving -1.5 + x = 15.882380174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 15.882380174 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 15.882380174 + 1.5 x = 15.882380174 + 1.5 Combine like terms: 15.882380174 + 1.5 = 17.382380174 x = 17.382380174 Simplifying x = 17.382380174Subproblem 2
x + -1.5 = -15.882380174 Simplifying x + -1.5 = -15.882380174 Reorder the terms: -1.5 + x = -15.882380174 Solving -1.5 + x = -15.882380174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -15.882380174 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -15.882380174 + 1.5 x = -15.882380174 + 1.5 Combine like terms: -15.882380174 + 1.5 = -14.382380174 x = -14.382380174 Simplifying x = -14.382380174Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.382380174, -14.382380174}Solution
x = {17.382380174, -14.382380174}
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