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Simplifying 0 = 0.7x2 + 0.2x + -1 Reorder the terms: 0 = -1 + 0.2x + 0.7x2 Solving 0 = -1 + 0.2x + 0.7x2 Solving for variable 'x'. Combine like terms: 0 + 1 = 1 1 + -0.2x + -0.7x2 = -1 + 0.2x + 0.7x2 + 1 + -0.2x + -0.7x2 Reorder the terms: 1 + -0.2x + -0.7x2 = -1 + 1 + 0.2x + -0.2x + 0.7x2 + -0.7x2 Combine like terms: -1 + 1 = 0 1 + -0.2x + -0.7x2 = 0 + 0.2x + -0.2x + 0.7x2 + -0.7x2 1 + -0.2x + -0.7x2 = 0.2x + -0.2x + 0.7x2 + -0.7x2 Combine like terms: 0.2x + -0.2x = 0.0 1 + -0.2x + -0.7x2 = 0.0 + 0.7x2 + -0.7x2 1 + -0.2x + -0.7x2 = 0.7x2 + -0.7x2 Combine like terms: 0.7x2 + -0.7x2 = 0.0 1 + -0.2x + -0.7x2 = 0.0 Begin completing the square. Divide all terms by -0.7 the coefficient of the squared term: Divide each side by '-0.7'. -1.428571429 + 0.2857142857x + x2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + 0.2857142857x + 1.428571429 + x2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + 0.2857142857x + x2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + 0.2857142857x + x2 = 0 + 1.428571429 0.2857142857x + x2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 0.2857142857x + x2 = 1.428571429 The x term is 0.2857142857x. Take half its coefficient (0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. 0.2857142857x + 0.02040816328 + x2 = 1.428571429 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857x + x2 = 1.428571429 + 0.02040816328 Combine like terms: 1.428571429 + 0.02040816328 = 1.44897959228 0.02040816328 + 0.2857142857x + x2 = 1.44897959228 Factor a perfect square on the left side: (x + 0.1428571429)(x + 0.1428571429) = 1.44897959228 Calculate the square root of the right side: 1.203735682 Break this problem into two subproblems by setting (x + 0.1428571429) equal to 1.203735682 and -1.203735682.Subproblem 1
x + 0.1428571429 = 1.203735682 Simplifying x + 0.1428571429 = 1.203735682 Reorder the terms: 0.1428571429 + x = 1.203735682 Solving 0.1428571429 + x = 1.203735682 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + x = 1.203735682 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = 1.203735682 + -0.1428571429 x = 1.203735682 + -0.1428571429 Combine like terms: 1.203735682 + -0.1428571429 = 1.0608785391 x = 1.0608785391 Simplifying x = 1.0608785391Subproblem 2
x + 0.1428571429 = -1.203735682 Simplifying x + 0.1428571429 = -1.203735682 Reorder the terms: 0.1428571429 + x = -1.203735682 Solving 0.1428571429 + x = -1.203735682 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + x = -1.203735682 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = -1.203735682 + -0.1428571429 x = -1.203735682 + -0.1428571429 Combine like terms: -1.203735682 + -0.1428571429 = -1.3465928249 x = -1.3465928249 Simplifying x = -1.3465928249Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0608785391, -1.3465928249}
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