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Simplifying 8x2 + 10x = -5x2 + 16 Reorder the terms: 10x + 8x2 = -5x2 + 16 Reorder the terms: 10x + 8x2 = 16 + -5x2 Solving 10x + 8x2 = 16 + -5x2 Solving for variable 'x'. Reorder the terms: -16 + 10x + 8x2 + 5x2 = 16 + -5x2 + -16 + 5x2 Combine like terms: 8x2 + 5x2 = 13x2 -16 + 10x + 13x2 = 16 + -5x2 + -16 + 5x2 Reorder the terms: -16 + 10x + 13x2 = 16 + -16 + -5x2 + 5x2 Combine like terms: 16 + -16 = 0 -16 + 10x + 13x2 = 0 + -5x2 + 5x2 -16 + 10x + 13x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -16 + 10x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -1.230769231 + 0.7692307692x + x2 = 0 Move the constant term to the right: Add '1.230769231' to each side of the equation. -1.230769231 + 0.7692307692x + 1.230769231 + x2 = 0 + 1.230769231 Reorder the terms: -1.230769231 + 1.230769231 + 0.7692307692x + x2 = 0 + 1.230769231 Combine like terms: -1.230769231 + 1.230769231 = 0.000000000 0.000000000 + 0.7692307692x + x2 = 0 + 1.230769231 0.7692307692x + x2 = 0 + 1.230769231 Combine like terms: 0 + 1.230769231 = 1.230769231 0.7692307692x + x2 = 1.230769231 The x term is 0.7692307692x. Take half its coefficient (0.3846153846). Square it (0.1479289941) and add it to both sides. Add '0.1479289941' to each side of the equation. 0.7692307692x + 0.1479289941 + x2 = 1.230769231 + 0.1479289941 Reorder the terms: 0.1479289941 + 0.7692307692x + x2 = 1.230769231 + 0.1479289941 Combine like terms: 1.230769231 + 0.1479289941 = 1.3786982251 0.1479289941 + 0.7692307692x + x2 = 1.3786982251 Factor a perfect square on the left side: (x + 0.3846153846)(x + 0.3846153846) = 1.3786982251 Calculate the square root of the right side: 1.17417981 Break this problem into two subproblems by setting (x + 0.3846153846) equal to 1.17417981 and -1.17417981.Subproblem 1
x + 0.3846153846 = 1.17417981 Simplifying x + 0.3846153846 = 1.17417981 Reorder the terms: 0.3846153846 + x = 1.17417981 Solving 0.3846153846 + x = 1.17417981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3846153846' to each side of the equation. 0.3846153846 + -0.3846153846 + x = 1.17417981 + -0.3846153846 Combine like terms: 0.3846153846 + -0.3846153846 = 0.0000000000 0.0000000000 + x = 1.17417981 + -0.3846153846 x = 1.17417981 + -0.3846153846 Combine like terms: 1.17417981 + -0.3846153846 = 0.7895644254 x = 0.7895644254 Simplifying x = 0.7895644254Subproblem 2
x + 0.3846153846 = -1.17417981 Simplifying x + 0.3846153846 = -1.17417981 Reorder the terms: 0.3846153846 + x = -1.17417981 Solving 0.3846153846 + x = -1.17417981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3846153846' to each side of the equation. 0.3846153846 + -0.3846153846 + x = -1.17417981 + -0.3846153846 Combine like terms: 0.3846153846 + -0.3846153846 = 0.0000000000 0.0000000000 + x = -1.17417981 + -0.3846153846 x = -1.17417981 + -0.3846153846 Combine like terms: -1.17417981 + -0.3846153846 = -1.5587951946 x = -1.5587951946 Simplifying x = -1.5587951946Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7895644254, -1.5587951946}
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