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Simplifying 12x2 + -7x + -8 = 5 Reorder the terms: -8 + -7x + 12x2 = 5 Solving -8 + -7x + 12x2 = 5 Solving for variable 'x'. Reorder the terms: -8 + -5 + -7x + 12x2 = 5 + -5 Combine like terms: -8 + -5 = -13 -13 + -7x + 12x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -13 + -7x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1.083333333 + -0.5833333333x + x2 = 0 Move the constant term to the right: Add '1.083333333' to each side of the equation. -1.083333333 + -0.5833333333x + 1.083333333 + x2 = 0 + 1.083333333 Reorder the terms: -1.083333333 + 1.083333333 + -0.5833333333x + x2 = 0 + 1.083333333 Combine like terms: -1.083333333 + 1.083333333 = 0.000000000 0.000000000 + -0.5833333333x + x2 = 0 + 1.083333333 -0.5833333333x + x2 = 0 + 1.083333333 Combine like terms: 0 + 1.083333333 = 1.083333333 -0.5833333333x + x2 = 1.083333333 The x term is -0.5833333333x. Take half its coefficient (-0.2916666667). Square it (0.08506944446) and add it to both sides. Add '0.08506944446' to each side of the equation. -0.5833333333x + 0.08506944446 + x2 = 1.083333333 + 0.08506944446 Reorder the terms: 0.08506944446 + -0.5833333333x + x2 = 1.083333333 + 0.08506944446 Combine like terms: 1.083333333 + 0.08506944446 = 1.16840277746 0.08506944446 + -0.5833333333x + x2 = 1.16840277746 Factor a perfect square on the left side: (x + -0.2916666667)(x + -0.2916666667) = 1.16840277746 Calculate the square root of the right side: 1.080926814 Break this problem into two subproblems by setting (x + -0.2916666667) equal to 1.080926814 and -1.080926814.Subproblem 1
x + -0.2916666667 = 1.080926814 Simplifying x + -0.2916666667 = 1.080926814 Reorder the terms: -0.2916666667 + x = 1.080926814 Solving -0.2916666667 + x = 1.080926814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2916666667' to each side of the equation. -0.2916666667 + 0.2916666667 + x = 1.080926814 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + x = 1.080926814 + 0.2916666667 x = 1.080926814 + 0.2916666667 Combine like terms: 1.080926814 + 0.2916666667 = 1.3725934807 x = 1.3725934807 Simplifying x = 1.3725934807Subproblem 2
x + -0.2916666667 = -1.080926814 Simplifying x + -0.2916666667 = -1.080926814 Reorder the terms: -0.2916666667 + x = -1.080926814 Solving -0.2916666667 + x = -1.080926814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2916666667' to each side of the equation. -0.2916666667 + 0.2916666667 + x = -1.080926814 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + x = -1.080926814 + 0.2916666667 x = -1.080926814 + 0.2916666667 Combine like terms: -1.080926814 + 0.2916666667 = -0.7892601473 x = -0.7892601473 Simplifying x = -0.7892601473Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3725934807, -0.7892601473}
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