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Simplifying 8x2 + -5x + -21 = 0 Reorder the terms: -21 + -5x + 8x2 = 0 Solving -21 + -5x + 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'. -2.625 + -0.625x + x2 = 0 Move the constant term to the right: Add '2.625' to each side of the equation. -2.625 + -0.625x + 2.625 + x2 = 0 + 2.625 Reorder the terms: -2.625 + 2.625 + -0.625x + x2 = 0 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + -0.625x + x2 = 0 + 2.625 -0.625x + x2 = 0 + 2.625 Combine like terms: 0 + 2.625 = 2.625 -0.625x + x2 = 2.625 The x term is -0.625x. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625x + 0.09765625 + x2 = 2.625 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = 2.625 + 0.09765625 Combine like terms: 2.625 + 0.09765625 = 2.72265625 0.09765625 + -0.625x + x2 = 2.72265625 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = 2.72265625 Calculate the square root of the right side: 1.650047348 Break this problem into two subproblems by setting (x + -0.3125) equal to 1.650047348 and -1.650047348.Subproblem 1
x + -0.3125 = 1.650047348 Simplifying x + -0.3125 = 1.650047348 Reorder the terms: -0.3125 + x = 1.650047348 Solving -0.3125 + x = 1.650047348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = 1.650047348 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 1.650047348 + 0.3125 x = 1.650047348 + 0.3125 Combine like terms: 1.650047348 + 0.3125 = 1.962547348 x = 1.962547348 Simplifying x = 1.962547348Subproblem 2
x + -0.3125 = -1.650047348 Simplifying x + -0.3125 = -1.650047348 Reorder the terms: -0.3125 + x = -1.650047348 Solving -0.3125 + x = -1.650047348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = -1.650047348 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -1.650047348 + 0.3125 x = -1.650047348 + 0.3125 Combine like terms: -1.650047348 + 0.3125 = -1.337547348 x = -1.337547348 Simplifying x = -1.337547348Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.962547348, -1.337547348}
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