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Simplifying 8x2 + 27x = 7 Reorder the terms: 27x + 8x2 = 7 Solving 27x + 8x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + 27x + 8x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 27x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.875 + 3.375x + x2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + 3.375x + 0.875 + x2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + 3.375x + x2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + 3.375x + x2 = 0 + 0.875 3.375x + x2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 3.375x + x2 = 0.875 The x term is 3.375x. Take half its coefficient (1.6875). Square it (2.84765625) and add it to both sides. Add '2.84765625' to each side of the equation. 3.375x + 2.84765625 + x2 = 0.875 + 2.84765625 Reorder the terms: 2.84765625 + 3.375x + x2 = 0.875 + 2.84765625 Combine like terms: 0.875 + 2.84765625 = 3.72265625 2.84765625 + 3.375x + x2 = 3.72265625 Factor a perfect square on the left side: (x + 1.6875)(x + 1.6875) = 3.72265625 Calculate the square root of the right side: 1.92941863 Break this problem into two subproblems by setting (x + 1.6875) equal to 1.92941863 and -1.92941863.Subproblem 1
x + 1.6875 = 1.92941863 Simplifying x + 1.6875 = 1.92941863 Reorder the terms: 1.6875 + x = 1.92941863 Solving 1.6875 + x = 1.92941863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6875' to each side of the equation. 1.6875 + -1.6875 + x = 1.92941863 + -1.6875 Combine like terms: 1.6875 + -1.6875 = 0.0000 0.0000 + x = 1.92941863 + -1.6875 x = 1.92941863 + -1.6875 Combine like terms: 1.92941863 + -1.6875 = 0.24191863 x = 0.24191863 Simplifying x = 0.24191863Subproblem 2
x + 1.6875 = -1.92941863 Simplifying x + 1.6875 = -1.92941863 Reorder the terms: 1.6875 + x = -1.92941863 Solving 1.6875 + x = -1.92941863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6875' to each side of the equation. 1.6875 + -1.6875 + x = -1.92941863 + -1.6875 Combine like terms: 1.6875 + -1.6875 = 0.0000 0.0000 + x = -1.92941863 + -1.6875 x = -1.92941863 + -1.6875 Combine like terms: -1.92941863 + -1.6875 = -3.61691863 x = -3.61691863 Simplifying x = -3.61691863Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.24191863, -3.61691863}
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