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Simplifying -8x2 + 13x = -61 Reorder the terms: 13x + -8x2 = -61 Solving 13x + -8x2 = -61 Solving for variable 'x'. Reorder the terms: 61 + 13x + -8x2 = -61 + 61 Combine like terms: -61 + 61 = 0 61 + 13x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -7.625 + -1.625x + x2 = 0 Move the constant term to the right: Add '7.625' to each side of the equation. -7.625 + -1.625x + 7.625 + x2 = 0 + 7.625 Reorder the terms: -7.625 + 7.625 + -1.625x + x2 = 0 + 7.625 Combine like terms: -7.625 + 7.625 = 0.000 0.000 + -1.625x + x2 = 0 + 7.625 -1.625x + x2 = 0 + 7.625 Combine like terms: 0 + 7.625 = 7.625 -1.625x + x2 = 7.625 The x term is -1.625x. Take half its coefficient (-0.8125). Square it (0.66015625) and add it to both sides. Add '0.66015625' to each side of the equation. -1.625x + 0.66015625 + x2 = 7.625 + 0.66015625 Reorder the terms: 0.66015625 + -1.625x + x2 = 7.625 + 0.66015625 Combine like terms: 7.625 + 0.66015625 = 8.28515625 0.66015625 + -1.625x + x2 = 8.28515625 Factor a perfect square on the left side: (x + -0.8125)(x + -0.8125) = 8.28515625 Calculate the square root of the right side: 2.878394735 Break this problem into two subproblems by setting (x + -0.8125) equal to 2.878394735 and -2.878394735.Subproblem 1
x + -0.8125 = 2.878394735 Simplifying x + -0.8125 = 2.878394735 Reorder the terms: -0.8125 + x = 2.878394735 Solving -0.8125 + x = 2.878394735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8125' to each side of the equation. -0.8125 + 0.8125 + x = 2.878394735 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + x = 2.878394735 + 0.8125 x = 2.878394735 + 0.8125 Combine like terms: 2.878394735 + 0.8125 = 3.690894735 x = 3.690894735 Simplifying x = 3.690894735Subproblem 2
x + -0.8125 = -2.878394735 Simplifying x + -0.8125 = -2.878394735 Reorder the terms: -0.8125 + x = -2.878394735 Solving -0.8125 + x = -2.878394735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8125' to each side of the equation. -0.8125 + 0.8125 + x = -2.878394735 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + x = -2.878394735 + 0.8125 x = -2.878394735 + 0.8125 Combine like terms: -2.878394735 + 0.8125 = -2.065894735 x = -2.065894735 Simplifying x = -2.065894735Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.690894735, -2.065894735}
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