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Simplifying -15x2 + -8x + 27 = 0 Reorder the terms: 27 + -8x + -15x2 = 0 Solving 27 + -8x + -15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. -1.8 + 0.5333333333x + x2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 0.5333333333x + 1.8 + x2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + 0.5333333333x + x2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 0.5333333333x + x2 = 0 + 1.8 0.5333333333x + x2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 0.5333333333x + x2 = 1.8 The x term is 0.5333333333x. Take half its coefficient (0.2666666667). Square it (0.07111111113) and add it to both sides. Add '0.07111111113' to each side of the equation. 0.5333333333x + 0.07111111113 + x2 = 1.8 + 0.07111111113 Reorder the terms: 0.07111111113 + 0.5333333333x + x2 = 1.8 + 0.07111111113 Combine like terms: 1.8 + 0.07111111113 = 1.87111111113 0.07111111113 + 0.5333333333x + x2 = 1.87111111113 Factor a perfect square on the left side: (x + 0.2666666667)(x + 0.2666666667) = 1.87111111113 Calculate the square root of the right side: 1.367885635 Break this problem into two subproblems by setting (x + 0.2666666667) equal to 1.367885635 and -1.367885635.Subproblem 1
x + 0.2666666667 = 1.367885635 Simplifying x + 0.2666666667 = 1.367885635 Reorder the terms: 0.2666666667 + x = 1.367885635 Solving 0.2666666667 + x = 1.367885635 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2666666667' to each side of the equation. 0.2666666667 + -0.2666666667 + x = 1.367885635 + -0.2666666667 Combine like terms: 0.2666666667 + -0.2666666667 = 0.0000000000 0.0000000000 + x = 1.367885635 + -0.2666666667 x = 1.367885635 + -0.2666666667 Combine like terms: 1.367885635 + -0.2666666667 = 1.1012189683 x = 1.1012189683 Simplifying x = 1.1012189683Subproblem 2
x + 0.2666666667 = -1.367885635 Simplifying x + 0.2666666667 = -1.367885635 Reorder the terms: 0.2666666667 + x = -1.367885635 Solving 0.2666666667 + x = -1.367885635 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2666666667' to each side of the equation. 0.2666666667 + -0.2666666667 + x = -1.367885635 + -0.2666666667 Combine like terms: 0.2666666667 + -0.2666666667 = 0.0000000000 0.0000000000 + x = -1.367885635 + -0.2666666667 x = -1.367885635 + -0.2666666667 Combine like terms: -1.367885635 + -0.2666666667 = -1.6345523017 x = -1.6345523017 Simplifying x = -1.6345523017Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1012189683, -1.6345523017}
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