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Simplifying (7x2 + -2x + -60) + (4x2 + 8x) = 0 Reorder the terms: (-60 + -2x + 7x2) + (4x2 + 8x) = 0 Remove parenthesis around (-60 + -2x + 7x2) -60 + -2x + 7x2 + (4x2 + 8x) = 0 Reorder the terms: -60 + -2x + 7x2 + (8x + 4x2) = 0 Remove parenthesis around (8x + 4x2) -60 + -2x + 7x2 + 8x + 4x2 = 0 Reorder the terms: -60 + -2x + 8x + 7x2 + 4x2 = 0 Combine like terms: -2x + 8x = 6x -60 + 6x + 7x2 + 4x2 = 0 Combine like terms: 7x2 + 4x2 = 11x2 -60 + 6x + 11x2 = 0 Solving -60 + 6x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -5.454545455 + 0.5454545455x + x2 = 0 Move the constant term to the right: Add '5.454545455' to each side of the equation. -5.454545455 + 0.5454545455x + 5.454545455 + x2 = 0 + 5.454545455 Reorder the terms: -5.454545455 + 5.454545455 + 0.5454545455x + x2 = 0 + 5.454545455 Combine like terms: -5.454545455 + 5.454545455 = 0.000000000 0.000000000 + 0.5454545455x + x2 = 0 + 5.454545455 0.5454545455x + x2 = 0 + 5.454545455 Combine like terms: 0 + 5.454545455 = 5.454545455 0.5454545455x + x2 = 5.454545455 The x term is 0.5454545455x. Take half its coefficient (0.2727272728). Square it (0.07438016533) and add it to both sides. Add '0.07438016533' to each side of the equation. 0.5454545455x + 0.07438016533 + x2 = 5.454545455 + 0.07438016533 Reorder the terms: 0.07438016533 + 0.5454545455x + x2 = 5.454545455 + 0.07438016533 Combine like terms: 5.454545455 + 0.07438016533 = 5.52892562033 0.07438016533 + 0.5454545455x + x2 = 5.52892562033 Factor a perfect square on the left side: (x + 0.2727272728)(x + 0.2727272728) = 5.52892562033 Calculate the square root of the right side: 2.351366756 Break this problem into two subproblems by setting (x + 0.2727272728) equal to 2.351366756 and -2.351366756.Subproblem 1
x + 0.2727272728 = 2.351366756 Simplifying x + 0.2727272728 = 2.351366756 Reorder the terms: 0.2727272728 + x = 2.351366756 Solving 0.2727272728 + x = 2.351366756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2727272728' to each side of the equation. 0.2727272728 + -0.2727272728 + x = 2.351366756 + -0.2727272728 Combine like terms: 0.2727272728 + -0.2727272728 = 0.0000000000 0.0000000000 + x = 2.351366756 + -0.2727272728 x = 2.351366756 + -0.2727272728 Combine like terms: 2.351366756 + -0.2727272728 = 2.0786394832 x = 2.0786394832 Simplifying x = 2.0786394832Subproblem 2
x + 0.2727272728 = -2.351366756 Simplifying x + 0.2727272728 = -2.351366756 Reorder the terms: 0.2727272728 + x = -2.351366756 Solving 0.2727272728 + x = -2.351366756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2727272728' to each side of the equation. 0.2727272728 + -0.2727272728 + x = -2.351366756 + -0.2727272728 Combine like terms: 0.2727272728 + -0.2727272728 = 0.0000000000 0.0000000000 + x = -2.351366756 + -0.2727272728 x = -2.351366756 + -0.2727272728 Combine like terms: -2.351366756 + -0.2727272728 = -2.6240940288 x = -2.6240940288 Simplifying x = -2.6240940288Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.0786394832, -2.6240940288}
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