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Simplifying -12x2 + 36.6x + 215.6328 = 0 Reorder the terms: 215.6328 + 36.6x + -12x2 = 0 Solving 215.6328 + 36.6x + -12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -17.9694 + -3.05x + x2 = 0 Move the constant term to the right: Add '17.9694' to each side of the equation. -17.9694 + -3.05x + 17.9694 + x2 = 0 + 17.9694 Reorder the terms: -17.9694 + 17.9694 + -3.05x + x2 = 0 + 17.9694 Combine like terms: -17.9694 + 17.9694 = 0.0000 0.0000 + -3.05x + x2 = 0 + 17.9694 -3.05x + x2 = 0 + 17.9694 Combine like terms: 0 + 17.9694 = 17.9694 -3.05x + x2 = 17.9694 The x term is -3.05x. Take half its coefficient (-1.525). Square it (2.325625) and add it to both sides. Add '2.325625' to each side of the equation. -3.05x + 2.325625 + x2 = 17.9694 + 2.325625 Reorder the terms: 2.325625 + -3.05x + x2 = 17.9694 + 2.325625 Combine like terms: 17.9694 + 2.325625 = 20.295025 2.325625 + -3.05x + x2 = 20.295025 Factor a perfect square on the left side: (x + -1.525)(x + -1.525) = 20.295025 Calculate the square root of the right side: 4.505 Break this problem into two subproblems by setting (x + -1.525) equal to 4.505 and -4.505.Subproblem 1
x + -1.525 = 4.505 Simplifying x + -1.525 = 4.505 Reorder the terms: -1.525 + x = 4.505 Solving -1.525 + x = 4.505 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.525' to each side of the equation. -1.525 + 1.525 + x = 4.505 + 1.525 Combine like terms: -1.525 + 1.525 = 0.000 0.000 + x = 4.505 + 1.525 x = 4.505 + 1.525 Combine like terms: 4.505 + 1.525 = 6.03 x = 6.03 Simplifying x = 6.03Subproblem 2
x + -1.525 = -4.505 Simplifying x + -1.525 = -4.505 Reorder the terms: -1.525 + x = -4.505 Solving -1.525 + x = -4.505 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.525' to each side of the equation. -1.525 + 1.525 + x = -4.505 + 1.525 Combine like terms: -1.525 + 1.525 = 0.000 0.000 + x = -4.505 + 1.525 x = -4.505 + 1.525 Combine like terms: -4.505 + 1.525 = -2.98 x = -2.98 Simplifying x = -2.98Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.03, -2.98}
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