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Simplifying 28x2 + 2x + -3 = 0 Reorder the terms: -3 + 2x + 28x2 = 0 Solving -3 + 2x + 28x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -0.1071428571 + 0.07142857143x + x2 = 0 Move the constant term to the right: Add '0.1071428571' to each side of the equation. -0.1071428571 + 0.07142857143x + 0.1071428571 + x2 = 0 + 0.1071428571 Reorder the terms: -0.1071428571 + 0.1071428571 + 0.07142857143x + x2 = 0 + 0.1071428571 Combine like terms: -0.1071428571 + 0.1071428571 = 0.0000000000 0.0000000000 + 0.07142857143x + x2 = 0 + 0.1071428571 0.07142857143x + x2 = 0 + 0.1071428571 Combine like terms: 0 + 0.1071428571 = 0.1071428571 0.07142857143x + x2 = 0.1071428571 The x term is 0.07142857143x. Take half its coefficient (0.03571428572). Square it (0.001275510204) and add it to both sides. Add '0.001275510204' to each side of the equation. 0.07142857143x + 0.001275510204 + x2 = 0.1071428571 + 0.001275510204 Reorder the terms: 0.001275510204 + 0.07142857143x + x2 = 0.1071428571 + 0.001275510204 Combine like terms: 0.1071428571 + 0.001275510204 = 0.108418367304 0.001275510204 + 0.07142857143x + x2 = 0.108418367304 Factor a perfect square on the left side: (x + 0.03571428572)(x + 0.03571428572) = 0.108418367304 Calculate the square root of the right side: 0.329269445 Break this problem into two subproblems by setting (x + 0.03571428572) equal to 0.329269445 and -0.329269445.Subproblem 1
x + 0.03571428572 = 0.329269445 Simplifying x + 0.03571428572 = 0.329269445 Reorder the terms: 0.03571428572 + x = 0.329269445 Solving 0.03571428572 + x = 0.329269445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03571428572' to each side of the equation. 0.03571428572 + -0.03571428572 + x = 0.329269445 + -0.03571428572 Combine like terms: 0.03571428572 + -0.03571428572 = 0.00000000000 0.00000000000 + x = 0.329269445 + -0.03571428572 x = 0.329269445 + -0.03571428572 Combine like terms: 0.329269445 + -0.03571428572 = 0.29355515928 x = 0.29355515928 Simplifying x = 0.29355515928Subproblem 2
x + 0.03571428572 = -0.329269445 Simplifying x + 0.03571428572 = -0.329269445 Reorder the terms: 0.03571428572 + x = -0.329269445 Solving 0.03571428572 + x = -0.329269445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03571428572' to each side of the equation. 0.03571428572 + -0.03571428572 + x = -0.329269445 + -0.03571428572 Combine like terms: 0.03571428572 + -0.03571428572 = 0.00000000000 0.00000000000 + x = -0.329269445 + -0.03571428572 x = -0.329269445 + -0.03571428572 Combine like terms: -0.329269445 + -0.03571428572 = -0.36498373072 x = -0.36498373072 Simplifying x = -0.36498373072Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.29355515928, -0.36498373072}
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