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Simplifying 8x2 + 4x + -27 = 0 Reorder the terms: -27 + 4x + 8x2 = 0 Solving -27 + 4x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.375 + 0.5x + x2 = 0 Move the constant term to the right: Add '3.375' to each side of the equation. -3.375 + 0.5x + 3.375 + x2 = 0 + 3.375 Reorder the terms: -3.375 + 3.375 + 0.5x + x2 = 0 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + 0.5x + x2 = 0 + 3.375 0.5x + x2 = 0 + 3.375 Combine like terms: 0 + 3.375 = 3.375 0.5x + x2 = 3.375 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 3.375 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 3.375 + 0.0625 Combine like terms: 3.375 + 0.0625 = 3.4375 0.0625 + 0.5x + x2 = 3.4375 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 3.4375 Calculate the square root of the right side: 1.854049622 Break this problem into two subproblems by setting (x + 0.25) equal to 1.854049622 and -1.854049622.Subproblem 1
x + 0.25 = 1.854049622 Simplifying x + 0.25 = 1.854049622 Reorder the terms: 0.25 + x = 1.854049622 Solving 0.25 + x = 1.854049622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.854049622 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.854049622 + -0.25 x = 1.854049622 + -0.25 Combine like terms: 1.854049622 + -0.25 = 1.604049622 x = 1.604049622 Simplifying x = 1.604049622Subproblem 2
x + 0.25 = -1.854049622 Simplifying x + 0.25 = -1.854049622 Reorder the terms: 0.25 + x = -1.854049622 Solving 0.25 + x = -1.854049622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.854049622 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.854049622 + -0.25 x = -1.854049622 + -0.25 Combine like terms: -1.854049622 + -0.25 = -2.104049622 x = -2.104049622 Simplifying x = -2.104049622Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.604049622, -2.104049622}
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