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Simplifying 32x2 + -5x + -12 = 0 Reorder the terms: -12 + -5x + 32x2 = 0 Solving -12 + -5x + 32x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -0.375 + -0.15625x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -0.15625x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -0.15625x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -0.15625x + x2 = 0 + 0.375 -0.15625x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -0.15625x + x2 = 0.375 The x term is -0.15625x. Take half its coefficient (-0.078125). Square it (0.006103515625) and add it to both sides. Add '0.006103515625' to each side of the equation. -0.15625x + 0.006103515625 + x2 = 0.375 + 0.006103515625 Reorder the terms: 0.006103515625 + -0.15625x + x2 = 0.375 + 0.006103515625 Combine like terms: 0.375 + 0.006103515625 = 0.381103515625 0.006103515625 + -0.15625x + x2 = 0.381103515625 Factor a perfect square on the left side: (x + -0.078125)(x + -0.078125) = 0.381103515625 Calculate the square root of the right side: 0.617335821 Break this problem into two subproblems by setting (x + -0.078125) equal to 0.617335821 and -0.617335821.Subproblem 1
x + -0.078125 = 0.617335821 Simplifying x + -0.078125 = 0.617335821 Reorder the terms: -0.078125 + x = 0.617335821 Solving -0.078125 + x = 0.617335821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.078125' to each side of the equation. -0.078125 + 0.078125 + x = 0.617335821 + 0.078125 Combine like terms: -0.078125 + 0.078125 = 0.000000 0.000000 + x = 0.617335821 + 0.078125 x = 0.617335821 + 0.078125 Combine like terms: 0.617335821 + 0.078125 = 0.695460821 x = 0.695460821 Simplifying x = 0.695460821Subproblem 2
x + -0.078125 = -0.617335821 Simplifying x + -0.078125 = -0.617335821 Reorder the terms: -0.078125 + x = -0.617335821 Solving -0.078125 + x = -0.617335821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.078125' to each side of the equation. -0.078125 + 0.078125 + x = -0.617335821 + 0.078125 Combine like terms: -0.078125 + 0.078125 = 0.000000 0.000000 + x = -0.617335821 + 0.078125 x = -0.617335821 + 0.078125 Combine like terms: -0.617335821 + 0.078125 = -0.539210821 x = -0.539210821 Simplifying x = -0.539210821Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.695460821, -0.539210821}
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