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Simplifying 3x2 + -70x + 300 = 0 Reorder the terms: 300 + -70x + 3x2 = 0 Solving 300 + -70x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 100 + -23.33333333x + x2 = 0 Move the constant term to the right: Add '-100' to each side of the equation. 100 + -23.33333333x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + -23.33333333x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -23.33333333x + x2 = 0 + -100 -23.33333333x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 -23.33333333x + x2 = -100 The x term is -23.33333333x. Take half its coefficient (-11.66666667). Square it (136.1111112) and add it to both sides. Add '136.1111112' to each side of the equation. -23.33333333x + 136.1111112 + x2 = -100 + 136.1111112 Reorder the terms: 136.1111112 + -23.33333333x + x2 = -100 + 136.1111112 Combine like terms: -100 + 136.1111112 = 36.1111112 136.1111112 + -23.33333333x + x2 = 36.1111112 Factor a perfect square on the left side: (x + -11.66666667)(x + -11.66666667) = 36.1111112 Calculate the square root of the right side: 6.009252133 Break this problem into two subproblems by setting (x + -11.66666667) equal to 6.009252133 and -6.009252133.Subproblem 1
x + -11.66666667 = 6.009252133 Simplifying x + -11.66666667 = 6.009252133 Reorder the terms: -11.66666667 + x = 6.009252133 Solving -11.66666667 + x = 6.009252133 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.66666667' to each side of the equation. -11.66666667 + 11.66666667 + x = 6.009252133 + 11.66666667 Combine like terms: -11.66666667 + 11.66666667 = 0.00000000 0.00000000 + x = 6.009252133 + 11.66666667 x = 6.009252133 + 11.66666667 Combine like terms: 6.009252133 + 11.66666667 = 17.675918803 x = 17.675918803 Simplifying x = 17.675918803Subproblem 2
x + -11.66666667 = -6.009252133 Simplifying x + -11.66666667 = -6.009252133 Reorder the terms: -11.66666667 + x = -6.009252133 Solving -11.66666667 + x = -6.009252133 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.66666667' to each side of the equation. -11.66666667 + 11.66666667 + x = -6.009252133 + 11.66666667 Combine like terms: -11.66666667 + 11.66666667 = 0.00000000 0.00000000 + x = -6.009252133 + 11.66666667 x = -6.009252133 + 11.66666667 Combine like terms: -6.009252133 + 11.66666667 = 5.657414537 x = 5.657414537 Simplifying x = 5.657414537Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.675918803, 5.657414537}
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