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Simplifying 28x2 + 9x = 2 Reorder the terms: 9x + 28x2 = 2 Solving 9x + 28x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + 9x + 28x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 9x + 28x2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -0.07142857143 + 0.3214285714x + x2 = 0 Move the constant term to the right: Add '0.07142857143' to each side of the equation. -0.07142857143 + 0.3214285714x + 0.07142857143 + x2 = 0 + 0.07142857143 Reorder the terms: -0.07142857143 + 0.07142857143 + 0.3214285714x + x2 = 0 + 0.07142857143 Combine like terms: -0.07142857143 + 0.07142857143 = 0.00000000000 0.00000000000 + 0.3214285714x + x2 = 0 + 0.07142857143 0.3214285714x + x2 = 0 + 0.07142857143 Combine like terms: 0 + 0.07142857143 = 0.07142857143 0.3214285714x + x2 = 0.07142857143 The x term is 0.3214285714x. Take half its coefficient (0.1607142857). Square it (0.02582908163) and add it to both sides. Add '0.02582908163' to each side of the equation. 0.3214285714x + 0.02582908163 + x2 = 0.07142857143 + 0.02582908163 Reorder the terms: 0.02582908163 + 0.3214285714x + x2 = 0.07142857143 + 0.02582908163 Combine like terms: 0.07142857143 + 0.02582908163 = 0.09725765306 0.02582908163 + 0.3214285714x + x2 = 0.09725765306 Factor a perfect square on the left side: (x + 0.1607142857)(x + 0.1607142857) = 0.09725765306 Calculate the square root of the right side: 0.311861593 Break this problem into two subproblems by setting (x + 0.1607142857) equal to 0.311861593 and -0.311861593.Subproblem 1
x + 0.1607142857 = 0.311861593 Simplifying x + 0.1607142857 = 0.311861593 Reorder the terms: 0.1607142857 + x = 0.311861593 Solving 0.1607142857 + x = 0.311861593 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1607142857' to each side of the equation. 0.1607142857 + -0.1607142857 + x = 0.311861593 + -0.1607142857 Combine like terms: 0.1607142857 + -0.1607142857 = 0.0000000000 0.0000000000 + x = 0.311861593 + -0.1607142857 x = 0.311861593 + -0.1607142857 Combine like terms: 0.311861593 + -0.1607142857 = 0.1511473073 x = 0.1511473073 Simplifying x = 0.1511473073Subproblem 2
x + 0.1607142857 = -0.311861593 Simplifying x + 0.1607142857 = -0.311861593 Reorder the terms: 0.1607142857 + x = -0.311861593 Solving 0.1607142857 + x = -0.311861593 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1607142857' to each side of the equation. 0.1607142857 + -0.1607142857 + x = -0.311861593 + -0.1607142857 Combine like terms: 0.1607142857 + -0.1607142857 = 0.0000000000 0.0000000000 + x = -0.311861593 + -0.1607142857 x = -0.311861593 + -0.1607142857 Combine like terms: -0.311861593 + -0.1607142857 = -0.4725758787 x = -0.4725758787 Simplifying x = -0.4725758787Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1511473073, -0.4725758787}
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