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Simplifying 7x2 + -60x + 80 = 0 Reorder the terms: 80 + -60x + 7x2 = 0 Solving 80 + -60x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 11.42857143 + -8.571428571x + x2 = 0 Move the constant term to the right: Add '-11.42857143' to each side of the equation. 11.42857143 + -8.571428571x + -11.42857143 + x2 = 0 + -11.42857143 Reorder the terms: 11.42857143 + -11.42857143 + -8.571428571x + x2 = 0 + -11.42857143 Combine like terms: 11.42857143 + -11.42857143 = 0.00000000 0.00000000 + -8.571428571x + x2 = 0 + -11.42857143 -8.571428571x + x2 = 0 + -11.42857143 Combine like terms: 0 + -11.42857143 = -11.42857143 -8.571428571x + x2 = -11.42857143 The x term is -8.571428571x. Take half its coefficient (-4.285714286). Square it (18.36734694) and add it to both sides. Add '18.36734694' to each side of the equation. -8.571428571x + 18.36734694 + x2 = -11.42857143 + 18.36734694 Reorder the terms: 18.36734694 + -8.571428571x + x2 = -11.42857143 + 18.36734694 Combine like terms: -11.42857143 + 18.36734694 = 6.93877551 18.36734694 + -8.571428571x + x2 = 6.93877551 Factor a perfect square on the left side: (x + -4.285714286)(x + -4.285714286) = 6.93877551 Calculate the square root of the right side: 2.634155559 Break this problem into two subproblems by setting (x + -4.285714286) equal to 2.634155559 and -2.634155559.Subproblem 1
x + -4.285714286 = 2.634155559 Simplifying x + -4.285714286 = 2.634155559 Reorder the terms: -4.285714286 + x = 2.634155559 Solving -4.285714286 + x = 2.634155559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.285714286' to each side of the equation. -4.285714286 + 4.285714286 + x = 2.634155559 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + x = 2.634155559 + 4.285714286 x = 2.634155559 + 4.285714286 Combine like terms: 2.634155559 + 4.285714286 = 6.919869845 x = 6.919869845 Simplifying x = 6.919869845Subproblem 2
x + -4.285714286 = -2.634155559 Simplifying x + -4.285714286 = -2.634155559 Reorder the terms: -4.285714286 + x = -2.634155559 Solving -4.285714286 + x = -2.634155559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.285714286' to each side of the equation. -4.285714286 + 4.285714286 + x = -2.634155559 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + x = -2.634155559 + 4.285714286 x = -2.634155559 + 4.285714286 Combine like terms: -2.634155559 + 4.285714286 = 1.651558727 x = 1.651558727 Simplifying x = 1.651558727Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.919869845, 1.651558727}
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