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Simplifying -27x2 + 2x + 225 = 0 Reorder the terms: 225 + 2x + -27x2 = 0 Solving 225 + 2x + -27x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -27 the coefficient of the squared term: Divide each side by '-27'. -8.333333333 + -0.07407407407x + x2 = 0 Move the constant term to the right: Add '8.333333333' to each side of the equation. -8.333333333 + -0.07407407407x + 8.333333333 + x2 = 0 + 8.333333333 Reorder the terms: -8.333333333 + 8.333333333 + -0.07407407407x + x2 = 0 + 8.333333333 Combine like terms: -8.333333333 + 8.333333333 = 0.000000000 0.000000000 + -0.07407407407x + x2 = 0 + 8.333333333 -0.07407407407x + x2 = 0 + 8.333333333 Combine like terms: 0 + 8.333333333 = 8.333333333 -0.07407407407x + x2 = 8.333333333 The x term is -0.07407407407x. Take half its coefficient (-0.03703703704). Square it (0.001371742113) and add it to both sides. Add '0.001371742113' to each side of the equation. -0.07407407407x + 0.001371742113 + x2 = 8.333333333 + 0.001371742113 Reorder the terms: 0.001371742113 + -0.07407407407x + x2 = 8.333333333 + 0.001371742113 Combine like terms: 8.333333333 + 0.001371742113 = 8.334705075113 0.001371742113 + -0.07407407407x + x2 = 8.334705075113 Factor a perfect square on the left side: (x + -0.03703703704)(x + -0.03703703704) = 8.334705075113 Calculate the square root of the right side: 2.886988929 Break this problem into two subproblems by setting (x + -0.03703703704) equal to 2.886988929 and -2.886988929.Subproblem 1
x + -0.03703703704 = 2.886988929 Simplifying x + -0.03703703704 = 2.886988929 Reorder the terms: -0.03703703704 + x = 2.886988929 Solving -0.03703703704 + x = 2.886988929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03703703704' to each side of the equation. -0.03703703704 + 0.03703703704 + x = 2.886988929 + 0.03703703704 Combine like terms: -0.03703703704 + 0.03703703704 = 0.00000000000 0.00000000000 + x = 2.886988929 + 0.03703703704 x = 2.886988929 + 0.03703703704 Combine like terms: 2.886988929 + 0.03703703704 = 2.92402596604 x = 2.92402596604 Simplifying x = 2.92402596604Subproblem 2
x + -0.03703703704 = -2.886988929 Simplifying x + -0.03703703704 = -2.886988929 Reorder the terms: -0.03703703704 + x = -2.886988929 Solving -0.03703703704 + x = -2.886988929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03703703704' to each side of the equation. -0.03703703704 + 0.03703703704 + x = -2.886988929 + 0.03703703704 Combine like terms: -0.03703703704 + 0.03703703704 = 0.00000000000 0.00000000000 + x = -2.886988929 + 0.03703703704 x = -2.886988929 + 0.03703703704 Combine like terms: -2.886988929 + 0.03703703704 = -2.84995189196 x = -2.84995189196 Simplifying x = -2.84995189196Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.92402596604, -2.84995189196}
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