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Simplifying 2x2 + -8x + -740 = 0 Reorder the terms: -740 + -8x + 2x2 = 0 Solving -740 + -8x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-370 + -4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-370 + -4x + x2)' equal to zero and attempt to solve: Simplifying -370 + -4x + x2 = 0 Solving -370 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '370' to each side of the equation. -370 + -4x + 370 + x2 = 0 + 370 Reorder the terms: -370 + 370 + -4x + x2 = 0 + 370 Combine like terms: -370 + 370 = 0 0 + -4x + x2 = 0 + 370 -4x + x2 = 0 + 370 Combine like terms: 0 + 370 = 370 -4x + x2 = 370 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 370 + 4 Reorder the terms: 4 + -4x + x2 = 370 + 4 Combine like terms: 370 + 4 = 374 4 + -4x + x2 = 374 Factor a perfect square on the left side: (x + -2)(x + -2) = 374 Calculate the square root of the right side: 19.339079606 Break this problem into two subproblems by setting (x + -2) equal to 19.339079606 and -19.339079606.Subproblem 1
x + -2 = 19.339079606 Simplifying x + -2 = 19.339079606 Reorder the terms: -2 + x = 19.339079606 Solving -2 + x = 19.339079606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 19.339079606 + 2 Combine like terms: -2 + 2 = 0 0 + x = 19.339079606 + 2 x = 19.339079606 + 2 Combine like terms: 19.339079606 + 2 = 21.339079606 x = 21.339079606 Simplifying x = 21.339079606Subproblem 2
x + -2 = -19.339079606 Simplifying x + -2 = -19.339079606 Reorder the terms: -2 + x = -19.339079606 Solving -2 + x = -19.339079606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -19.339079606 + 2 Combine like terms: -2 + 2 = 0 0 + x = -19.339079606 + 2 x = -19.339079606 + 2 Combine like terms: -19.339079606 + 2 = -17.339079606 x = -17.339079606 Simplifying x = -17.339079606Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.339079606, -17.339079606}Solution
x = {21.339079606, -17.339079606}
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