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Simplifying 11x2 + 30x = 124 Reorder the terms: 30x + 11x2 = 124 Solving 30x + 11x2 = 124 Solving for variable 'x'. Reorder the terms: -124 + 30x + 11x2 = 124 + -124 Combine like terms: 124 + -124 = 0 -124 + 30x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -11.27272727 + 2.727272727x + x2 = 0 Move the constant term to the right: Add '11.27272727' to each side of the equation. -11.27272727 + 2.727272727x + 11.27272727 + x2 = 0 + 11.27272727 Reorder the terms: -11.27272727 + 11.27272727 + 2.727272727x + x2 = 0 + 11.27272727 Combine like terms: -11.27272727 + 11.27272727 = 0.00000000 0.00000000 + 2.727272727x + x2 = 0 + 11.27272727 2.727272727x + x2 = 0 + 11.27272727 Combine like terms: 0 + 11.27272727 = 11.27272727 2.727272727x + x2 = 11.27272727 The x term is 2.727272727x. Take half its coefficient (1.363636364). Square it (1.859504133) and add it to both sides. Add '1.859504133' to each side of the equation. 2.727272727x + 1.859504133 + x2 = 11.27272727 + 1.859504133 Reorder the terms: 1.859504133 + 2.727272727x + x2 = 11.27272727 + 1.859504133 Combine like terms: 11.27272727 + 1.859504133 = 13.132231403 1.859504133 + 2.727272727x + x2 = 13.132231403 Factor a perfect square on the left side: (x + 1.363636364)(x + 1.363636364) = 13.132231403 Calculate the square root of the right side: 3.623842078 Break this problem into two subproblems by setting (x + 1.363636364) equal to 3.623842078 and -3.623842078.Subproblem 1
x + 1.363636364 = 3.623842078 Simplifying x + 1.363636364 = 3.623842078 Reorder the terms: 1.363636364 + x = 3.623842078 Solving 1.363636364 + x = 3.623842078 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.363636364' to each side of the equation. 1.363636364 + -1.363636364 + x = 3.623842078 + -1.363636364 Combine like terms: 1.363636364 + -1.363636364 = 0.000000000 0.000000000 + x = 3.623842078 + -1.363636364 x = 3.623842078 + -1.363636364 Combine like terms: 3.623842078 + -1.363636364 = 2.260205714 x = 2.260205714 Simplifying x = 2.260205714Subproblem 2
x + 1.363636364 = -3.623842078 Simplifying x + 1.363636364 = -3.623842078 Reorder the terms: 1.363636364 + x = -3.623842078 Solving 1.363636364 + x = -3.623842078 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.363636364' to each side of the equation. 1.363636364 + -1.363636364 + x = -3.623842078 + -1.363636364 Combine like terms: 1.363636364 + -1.363636364 = 0.000000000 0.000000000 + x = -3.623842078 + -1.363636364 x = -3.623842078 + -1.363636364 Combine like terms: -3.623842078 + -1.363636364 = -4.987478442 x = -4.987478442 Simplifying x = -4.987478442Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.260205714, -4.987478442}
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