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Simplifying -5x + 16 + -8x2 + 13 = 0 Reorder the terms: 16 + 13 + -5x + -8x2 = 0 Combine like terms: 16 + 13 = 29 29 + -5x + -8x2 = 0 Solving 29 + -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'. -3.625 + 0.625x + x2 = 0 Move the constant term to the right: Add '3.625' to each side of the equation. -3.625 + 0.625x + 3.625 + x2 = 0 + 3.625 Reorder the terms: -3.625 + 3.625 + 0.625x + x2 = 0 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + 0.625x + x2 = 0 + 3.625 0.625x + x2 = 0 + 3.625 Combine like terms: 0 + 3.625 = 3.625 0.625x + x2 = 3.625 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 = 3.625 + 0.09765625 Reorder the terms: 0.09765625 + 0.625x + x2 = 3.625 + 0.09765625 Combine like terms: 3.625 + 0.09765625 = 3.72265625 0.09765625 + 0.625x + x2 = 3.72265625 Factor a perfect square on the left side: (x + 0.3125)(x + 0.3125) = 3.72265625 Calculate the square root of the right side: 1.92941863 Break this problem into two subproblems by setting (x + 0.3125) equal to 1.92941863 and -1.92941863.Subproblem 1
x + 0.3125 = 1.92941863 Simplifying x + 0.3125 = 1.92941863 Reorder the terms: 0.3125 + x = 1.92941863 Solving 0.3125 + x = 1.92941863 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 = 1.92941863 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = 1.92941863 + -0.3125 x = 1.92941863 + -0.3125 Combine like terms: 1.92941863 + -0.3125 = 1.61691863 x = 1.61691863 Simplifying x = 1.61691863Subproblem 2
x + 0.3125 = -1.92941863 Simplifying x + 0.3125 = -1.92941863 Reorder the terms: 0.3125 + x = -1.92941863 Solving 0.3125 + x = -1.92941863 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 = -1.92941863 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = -1.92941863 + -0.3125 x = -1.92941863 + -0.3125 Combine like terms: -1.92941863 + -0.3125 = -2.24191863 x = -2.24191863 Simplifying x = -2.24191863Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.61691863, -2.24191863}
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