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Simplifying 7x + 120 = 2.75x2 Reorder the terms: 120 + 7x = 2.75x2 Solving 120 + 7x = 2.75x2 Solving for variable 'x'. Combine like terms: 2.75x2 + -2.75x2 = 0.00 120 + 7x + -2.75x2 = 0.00 Begin completing the square. Divide all terms by -2.75 the coefficient of the squared term: Divide each side by '-2.75'. -43.63636364 + -2.545454545x + x2 = 0 Move the constant term to the right: Add '43.63636364' to each side of the equation. -43.63636364 + -2.545454545x + 43.63636364 + x2 = 0 + 43.63636364 Reorder the terms: -43.63636364 + 43.63636364 + -2.545454545x + x2 = 0 + 43.63636364 Combine like terms: -43.63636364 + 43.63636364 = 0.00000000 0.00000000 + -2.545454545x + x2 = 0 + 43.63636364 -2.545454545x + x2 = 0 + 43.63636364 Combine like terms: 0 + 43.63636364 = 43.63636364 -2.545454545x + x2 = 43.63636364 The x term is -2.545454545x. Take half its coefficient (-1.272727273). Square it (1.619834711) and add it to both sides. Add '1.619834711' to each side of the equation. -2.545454545x + 1.619834711 + x2 = 43.63636364 + 1.619834711 Reorder the terms: 1.619834711 + -2.545454545x + x2 = 43.63636364 + 1.619834711 Combine like terms: 43.63636364 + 1.619834711 = 45.256198351 1.619834711 + -2.545454545x + x2 = 45.256198351 Factor a perfect square on the left side: (x + -1.272727273)(x + -1.272727273) = 45.256198351 Calculate the square root of the right side: 6.727272728 Break this problem into two subproblems by setting (x + -1.272727273) equal to 6.727272728 and -6.727272728.Subproblem 1
x + -1.272727273 = 6.727272728 Simplifying x + -1.272727273 = 6.727272728 Reorder the terms: -1.272727273 + x = 6.727272728 Solving -1.272727273 + x = 6.727272728 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.272727273' to each side of the equation. -1.272727273 + 1.272727273 + x = 6.727272728 + 1.272727273 Combine like terms: -1.272727273 + 1.272727273 = 0.000000000 0.000000000 + x = 6.727272728 + 1.272727273 x = 6.727272728 + 1.272727273 Combine like terms: 6.727272728 + 1.272727273 = 8.000000001 x = 8.000000001 Simplifying x = 8.000000001Subproblem 2
x + -1.272727273 = -6.727272728 Simplifying x + -1.272727273 = -6.727272728 Reorder the terms: -1.272727273 + x = -6.727272728 Solving -1.272727273 + x = -6.727272728 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.272727273' to each side of the equation. -1.272727273 + 1.272727273 + x = -6.727272728 + 1.272727273 Combine like terms: -1.272727273 + 1.272727273 = 0.000000000 0.000000000 + x = -6.727272728 + 1.272727273 x = -6.727272728 + 1.272727273 Combine like terms: -6.727272728 + 1.272727273 = -5.454545455 x = -5.454545455 Simplifying x = -5.454545455Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.000000001, -5.454545455}
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