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Simplifying 50x(10x + -40) = 20x + 350 Reorder the terms: 50x(-40 + 10x) = 20x + 350 (-40 * 50x + 10x * 50x) = 20x + 350 (-2000x + 500x2) = 20x + 350 Reorder the terms: -2000x + 500x2 = 350 + 20x Solving -2000x + 500x2 = 350 + 20x Solving for variable 'x'. Reorder the terms: -350 + -2000x + -20x + 500x2 = 350 + 20x + -350 + -20x Combine like terms: -2000x + -20x = -2020x -350 + -2020x + 500x2 = 350 + 20x + -350 + -20x Reorder the terms: -350 + -2020x + 500x2 = 350 + -350 + 20x + -20x Combine like terms: 350 + -350 = 0 -350 + -2020x + 500x2 = 0 + 20x + -20x -350 + -2020x + 500x2 = 20x + -20x Combine like terms: 20x + -20x = 0 -350 + -2020x + 500x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-35 + -202x + 50x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-35 + -202x + 50x2)' equal to zero and attempt to solve: Simplifying -35 + -202x + 50x2 = 0 Solving -35 + -202x + 50x2 = 0 Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. -0.7 + -4.04x + x2 = 0.0 Move the constant term to the right: Add '0.7' to each side of the equation. -0.7 + -4.04x + 0.7 + x2 = 0.0 + 0.7 Reorder the terms: -0.7 + 0.7 + -4.04x + x2 = 0.0 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + -4.04x + x2 = 0.0 + 0.7 -4.04x + x2 = 0.0 + 0.7 Combine like terms: 0.0 + 0.7 = 0.7 -4.04x + x2 = 0.7 The x term is -4.04x. Take half its coefficient (-2.02). Square it (4.0804) and add it to both sides. Add '4.0804' to each side of the equation. -4.04x + 4.0804 + x2 = 0.7 + 4.0804 Reorder the terms: 4.0804 + -4.04x + x2 = 0.7 + 4.0804 Combine like terms: 0.7 + 4.0804 = 4.7804 4.0804 + -4.04x + x2 = 4.7804 Factor a perfect square on the left side: (x + -2.02)(x + -2.02) = 4.7804 Calculate the square root of the right side: 2.186412587 Break this problem into two subproblems by setting (x + -2.02) equal to 2.186412587 and -2.186412587.Subproblem 1
x + -2.02 = 2.186412587 Simplifying x + -2.02 = 2.186412587 Reorder the terms: -2.02 + x = 2.186412587 Solving -2.02 + x = 2.186412587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.02' to each side of the equation. -2.02 + 2.02 + x = 2.186412587 + 2.02 Combine like terms: -2.02 + 2.02 = 0.00 0.00 + x = 2.186412587 + 2.02 x = 2.186412587 + 2.02 Combine like terms: 2.186412587 + 2.02 = 4.206412587 x = 4.206412587 Simplifying x = 4.206412587Subproblem 2
x + -2.02 = -2.186412587 Simplifying x + -2.02 = -2.186412587 Reorder the terms: -2.02 + x = -2.186412587 Solving -2.02 + x = -2.186412587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.02' to each side of the equation. -2.02 + 2.02 + x = -2.186412587 + 2.02 Combine like terms: -2.02 + 2.02 = 0.00 0.00 + x = -2.186412587 + 2.02 x = -2.186412587 + 2.02 Combine like terms: -2.186412587 + 2.02 = -0.166412587 x = -0.166412587 Simplifying x = -0.166412587Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.206412587, -0.166412587}Solution
x = {4.206412587, -0.166412587}
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