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Simplifying 7x2 + 0.8x + -1.7 = 0 Reorder the terms: -1.7 + 0.8x + 7x2 = 0 Solving -1.7 + 0.8x + 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'. -0.2428571429 + 0.1142857143x + x2 = 0 Move the constant term to the right: Add '0.2428571429' to each side of the equation. -0.2428571429 + 0.1142857143x + 0.2428571429 + x2 = 0 + 0.2428571429 Reorder the terms: -0.2428571429 + 0.2428571429 + 0.1142857143x + x2 = 0 + 0.2428571429 Combine like terms: -0.2428571429 + 0.2428571429 = 0.0000000000 0.0000000000 + 0.1142857143x + x2 = 0 + 0.2428571429 0.1142857143x + x2 = 0 + 0.2428571429 Combine like terms: 0 + 0.2428571429 = 0.2428571429 0.1142857143x + x2 = 0.2428571429 The x term is 0.1142857143x. Take half its coefficient (0.05714285715). Square it (0.003265306123) and add it to both sides. Add '0.003265306123' to each side of the equation. 0.1142857143x + 0.003265306123 + x2 = 0.2428571429 + 0.003265306123 Reorder the terms: 0.003265306123 + 0.1142857143x + x2 = 0.2428571429 + 0.003265306123 Combine like terms: 0.2428571429 + 0.003265306123 = 0.246122449023 0.003265306123 + 0.1142857143x + x2 = 0.246122449023 Factor a perfect square on the left side: (x + 0.05714285715)(x + 0.05714285715) = 0.246122449023 Calculate the square root of the right side: 0.496107296 Break this problem into two subproblems by setting (x + 0.05714285715) equal to 0.496107296 and -0.496107296.Subproblem 1
x + 0.05714285715 = 0.496107296 Simplifying x + 0.05714285715 = 0.496107296 Reorder the terms: 0.05714285715 + x = 0.496107296 Solving 0.05714285715 + x = 0.496107296 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05714285715' to each side of the equation. 0.05714285715 + -0.05714285715 + x = 0.496107296 + -0.05714285715 Combine like terms: 0.05714285715 + -0.05714285715 = 0.00000000000 0.00000000000 + x = 0.496107296 + -0.05714285715 x = 0.496107296 + -0.05714285715 Combine like terms: 0.496107296 + -0.05714285715 = 0.43896443885 x = 0.43896443885 Simplifying x = 0.43896443885Subproblem 2
x + 0.05714285715 = -0.496107296 Simplifying x + 0.05714285715 = -0.496107296 Reorder the terms: 0.05714285715 + x = -0.496107296 Solving 0.05714285715 + x = -0.496107296 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05714285715' to each side of the equation. 0.05714285715 + -0.05714285715 + x = -0.496107296 + -0.05714285715 Combine like terms: 0.05714285715 + -0.05714285715 = 0.00000000000 0.00000000000 + x = -0.496107296 + -0.05714285715 x = -0.496107296 + -0.05714285715 Combine like terms: -0.496107296 + -0.05714285715 = -0.55325015315 x = -0.55325015315 Simplifying x = -0.55325015315Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.43896443885, -0.55325015315}
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