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Simplifying 800 + -240x + 12x2 = 0 Solving 800 + -240x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(200 + -60x + 3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(200 + -60x + 3x2)' equal to zero and attempt to solve: Simplifying 200 + -60x + 3x2 = 0 Solving 200 + -60x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 66.66666667 + -20x + x2 = 0 Move the constant term to the right: Add '-66.66666667' to each side of the equation. 66.66666667 + -20x + -66.66666667 + x2 = 0 + -66.66666667 Reorder the terms: 66.66666667 + -66.66666667 + -20x + x2 = 0 + -66.66666667 Combine like terms: 66.66666667 + -66.66666667 = 0.00000000 0.00000000 + -20x + x2 = 0 + -66.66666667 -20x + x2 = 0 + -66.66666667 Combine like terms: 0 + -66.66666667 = -66.66666667 -20x + x2 = -66.66666667 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -66.66666667 + 100 Reorder the terms: 100 + -20x + x2 = -66.66666667 + 100 Combine like terms: -66.66666667 + 100 = 33.33333333 100 + -20x + x2 = 33.33333333 Factor a perfect square on the left side: (x + -10)(x + -10) = 33.33333333 Calculate the square root of the right side: 5.773502692 Break this problem into two subproblems by setting (x + -10) equal to 5.773502692 and -5.773502692.Subproblem 1
x + -10 = 5.773502692 Simplifying x + -10 = 5.773502692 Reorder the terms: -10 + x = 5.773502692 Solving -10 + x = 5.773502692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 5.773502692 + 10 Combine like terms: -10 + 10 = 0 0 + x = 5.773502692 + 10 x = 5.773502692 + 10 Combine like terms: 5.773502692 + 10 = 15.773502692 x = 15.773502692 Simplifying x = 15.773502692Subproblem 2
x + -10 = -5.773502692 Simplifying x + -10 = -5.773502692 Reorder the terms: -10 + x = -5.773502692 Solving -10 + x = -5.773502692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -5.773502692 + 10 Combine like terms: -10 + 10 = 0 0 + x = -5.773502692 + 10 x = -5.773502692 + 10 Combine like terms: -5.773502692 + 10 = 4.226497308 x = 4.226497308 Simplifying x = 4.226497308Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.773502692, 4.226497308}Solution
x = {15.773502692, 4.226497308}
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