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Simplifying 7x2 + -45x + 28 = 0 Reorder the terms: 28 + -45x + 7x2 = 0 Solving 28 + -45x + 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'. 4 + -6.428571429x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -6.428571429x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -6.428571429x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -6.428571429x + x2 = 0 + -4 -6.428571429x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -6.428571429x + x2 = -4 The x term is -6.428571429x. Take half its coefficient (-3.214285715). Square it (10.33163266) and add it to both sides. Add '10.33163266' to each side of the equation. -6.428571429x + 10.33163266 + x2 = -4 + 10.33163266 Reorder the terms: 10.33163266 + -6.428571429x + x2 = -4 + 10.33163266 Combine like terms: -4 + 10.33163266 = 6.33163266 10.33163266 + -6.428571429x + x2 = 6.33163266 Factor a perfect square on the left side: (x + -3.214285715)(x + -3.214285715) = 6.33163266 Calculate the square root of the right side: 2.516273566 Break this problem into two subproblems by setting (x + -3.214285715) equal to 2.516273566 and -2.516273566.Subproblem 1
x + -3.214285715 = 2.516273566 Simplifying x + -3.214285715 = 2.516273566 Reorder the terms: -3.214285715 + x = 2.516273566 Solving -3.214285715 + x = 2.516273566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.214285715' to each side of the equation. -3.214285715 + 3.214285715 + x = 2.516273566 + 3.214285715 Combine like terms: -3.214285715 + 3.214285715 = 0.000000000 0.000000000 + x = 2.516273566 + 3.214285715 x = 2.516273566 + 3.214285715 Combine like terms: 2.516273566 + 3.214285715 = 5.730559281 x = 5.730559281 Simplifying x = 5.730559281Subproblem 2
x + -3.214285715 = -2.516273566 Simplifying x + -3.214285715 = -2.516273566 Reorder the terms: -3.214285715 + x = -2.516273566 Solving -3.214285715 + x = -2.516273566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.214285715' to each side of the equation. -3.214285715 + 3.214285715 + x = -2.516273566 + 3.214285715 Combine like terms: -3.214285715 + 3.214285715 = 0.000000000 0.000000000 + x = -2.516273566 + 3.214285715 x = -2.516273566 + 3.214285715 Combine like terms: -2.516273566 + 3.214285715 = 0.698012149 x = 0.698012149 Simplifying x = 0.698012149Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.730559281, 0.698012149}
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