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Simplifying 8x2 + -21x + -90 = 0 Reorder the terms: -90 + -21x + 8x2 = 0 Solving -90 + -21x + 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'. -11.25 + -2.625x + x2 = 0 Move the constant term to the right: Add '11.25' to each side of the equation. -11.25 + -2.625x + 11.25 + x2 = 0 + 11.25 Reorder the terms: -11.25 + 11.25 + -2.625x + x2 = 0 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + -2.625x + x2 = 0 + 11.25 -2.625x + x2 = 0 + 11.25 Combine like terms: 0 + 11.25 = 11.25 -2.625x + x2 = 11.25 The x term is -2.625x. Take half its coefficient (-1.3125). Square it (1.72265625) and add it to both sides. Add '1.72265625' to each side of the equation. -2.625x + 1.72265625 + x2 = 11.25 + 1.72265625 Reorder the terms: 1.72265625 + -2.625x + x2 = 11.25 + 1.72265625 Combine like terms: 11.25 + 1.72265625 = 12.97265625 1.72265625 + -2.625x + x2 = 12.97265625 Factor a perfect square on the left side: (x + -1.3125)(x + -1.3125) = 12.97265625 Calculate the square root of the right side: 3.601757384 Break this problem into two subproblems by setting (x + -1.3125) equal to 3.601757384 and -3.601757384.Subproblem 1
x + -1.3125 = 3.601757384 Simplifying x + -1.3125 = 3.601757384 Reorder the terms: -1.3125 + x = 3.601757384 Solving -1.3125 + x = 3.601757384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3125' to each side of the equation. -1.3125 + 1.3125 + x = 3.601757384 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + x = 3.601757384 + 1.3125 x = 3.601757384 + 1.3125 Combine like terms: 3.601757384 + 1.3125 = 4.914257384 x = 4.914257384 Simplifying x = 4.914257384Subproblem 2
x + -1.3125 = -3.601757384 Simplifying x + -1.3125 = -3.601757384 Reorder the terms: -1.3125 + x = -3.601757384 Solving -1.3125 + x = -3.601757384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3125' to each side of the equation. -1.3125 + 1.3125 + x = -3.601757384 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + x = -3.601757384 + 1.3125 x = -3.601757384 + 1.3125 Combine like terms: -3.601757384 + 1.3125 = -2.289257384 x = -2.289257384 Simplifying x = -2.289257384Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.914257384, -2.289257384}
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