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Simplifying 3x2 + 70x + -1200 = 0 Reorder the terms: -1200 + 70x + 3x2 = 0 Solving -1200 + 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'. -400 + 23.33333333x + x2 = 0 Move the constant term to the right: Add '400' to each side of the equation. -400 + 23.33333333x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + 23.33333333x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + 23.33333333x + x2 = 0 + 400 23.33333333x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 23.33333333x + x2 = 400 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 = 400 + 136.1111112 Reorder the terms: 136.1111112 + 23.33333333x + x2 = 400 + 136.1111112 Combine like terms: 400 + 136.1111112 = 536.1111112 136.1111112 + 23.33333333x + x2 = 536.1111112 Factor a perfect square on the left side: (x + 11.66666667)(x + 11.66666667) = 536.1111112 Calculate the square root of the right side: 23.154073318 Break this problem into two subproblems by setting (x + 11.66666667) equal to 23.154073318 and -23.154073318.Subproblem 1
x + 11.66666667 = 23.154073318 Simplifying x + 11.66666667 = 23.154073318 Reorder the terms: 11.66666667 + x = 23.154073318 Solving 11.66666667 + x = 23.154073318 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 = 23.154073318 + -11.66666667 Combine like terms: 11.66666667 + -11.66666667 = 0.00000000 0.00000000 + x = 23.154073318 + -11.66666667 x = 23.154073318 + -11.66666667 Combine like terms: 23.154073318 + -11.66666667 = 11.487406648 x = 11.487406648 Simplifying x = 11.487406648Subproblem 2
x + 11.66666667 = -23.154073318 Simplifying x + 11.66666667 = -23.154073318 Reorder the terms: 11.66666667 + x = -23.154073318 Solving 11.66666667 + x = -23.154073318 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 = -23.154073318 + -11.66666667 Combine like terms: 11.66666667 + -11.66666667 = 0.00000000 0.00000000 + x = -23.154073318 + -11.66666667 x = -23.154073318 + -11.66666667 Combine like terms: -23.154073318 + -11.66666667 = -34.820739988 x = -34.820739988 Simplifying x = -34.820739988Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.487406648, -34.820739988}
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