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Simplifying 28x2 + -9x + -1 = 0 Reorder the terms: -1 + -9x + 28x2 = 0 Solving -1 + -9x + 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'. -0.03571428571 + -0.3214285714x + x2 = 0 Move the constant term to the right: Add '0.03571428571' to each side of the equation. -0.03571428571 + -0.3214285714x + 0.03571428571 + x2 = 0 + 0.03571428571 Reorder the terms: -0.03571428571 + 0.03571428571 + -0.3214285714x + x2 = 0 + 0.03571428571 Combine like terms: -0.03571428571 + 0.03571428571 = 0.00000000000 0.00000000000 + -0.3214285714x + x2 = 0 + 0.03571428571 -0.3214285714x + x2 = 0 + 0.03571428571 Combine like terms: 0 + 0.03571428571 = 0.03571428571 -0.3214285714x + x2 = 0.03571428571 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 = 0.03571428571 + 0.02582908163 Reorder the terms: 0.02582908163 + -0.3214285714x + x2 = 0.03571428571 + 0.02582908163 Combine like terms: 0.03571428571 + 0.02582908163 = 0.06154336734 0.02582908163 + -0.3214285714x + x2 = 0.06154336734 Factor a perfect square on the left side: (x + -0.1607142857)(x + -0.1607142857) = 0.06154336734 Calculate the square root of the right side: 0.248079357 Break this problem into two subproblems by setting (x + -0.1607142857) equal to 0.248079357 and -0.248079357.Subproblem 1
x + -0.1607142857 = 0.248079357 Simplifying x + -0.1607142857 = 0.248079357 Reorder the terms: -0.1607142857 + x = 0.248079357 Solving -0.1607142857 + x = 0.248079357 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 = 0.248079357 + 0.1607142857 Combine like terms: -0.1607142857 + 0.1607142857 = 0.0000000000 0.0000000000 + x = 0.248079357 + 0.1607142857 x = 0.248079357 + 0.1607142857 Combine like terms: 0.248079357 + 0.1607142857 = 0.4087936427 x = 0.4087936427 Simplifying x = 0.4087936427Subproblem 2
x + -0.1607142857 = -0.248079357 Simplifying x + -0.1607142857 = -0.248079357 Reorder the terms: -0.1607142857 + x = -0.248079357 Solving -0.1607142857 + x = -0.248079357 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 = -0.248079357 + 0.1607142857 Combine like terms: -0.1607142857 + 0.1607142857 = 0.0000000000 0.0000000000 + x = -0.248079357 + 0.1607142857 x = -0.248079357 + 0.1607142857 Combine like terms: -0.248079357 + 0.1607142857 = -0.0873650713 x = -0.0873650713 Simplifying x = -0.0873650713Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4087936427, -0.0873650713}
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