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Simplifying 8x2 + 51x + 54 = 0 Reorder the terms: 54 + 51x + 8x2 = 0 Solving 54 + 51x + 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'. 6.75 + 6.375x + x2 = 0 Move the constant term to the right: Add '-6.75' to each side of the equation. 6.75 + 6.375x + -6.75 + x2 = 0 + -6.75 Reorder the terms: 6.75 + -6.75 + 6.375x + x2 = 0 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + 6.375x + x2 = 0 + -6.75 6.375x + x2 = 0 + -6.75 Combine like terms: 0 + -6.75 = -6.75 6.375x + x2 = -6.75 The x term is 6.375x. Take half its coefficient (3.1875). Square it (10.16015625) and add it to both sides. Add '10.16015625' to each side of the equation. 6.375x + 10.16015625 + x2 = -6.75 + 10.16015625 Reorder the terms: 10.16015625 + 6.375x + x2 = -6.75 + 10.16015625 Combine like terms: -6.75 + 10.16015625 = 3.41015625 10.16015625 + 6.375x + x2 = 3.41015625 Factor a perfect square on the left side: (x + 3.1875)(x + 3.1875) = 3.41015625 Calculate the square root of the right side: 1.846660838 Break this problem into two subproblems by setting (x + 3.1875) equal to 1.846660838 and -1.846660838.Subproblem 1
x + 3.1875 = 1.846660838 Simplifying x + 3.1875 = 1.846660838 Reorder the terms: 3.1875 + x = 1.846660838 Solving 3.1875 + x = 1.846660838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.1875' to each side of the equation. 3.1875 + -3.1875 + x = 1.846660838 + -3.1875 Combine like terms: 3.1875 + -3.1875 = 0.0000 0.0000 + x = 1.846660838 + -3.1875 x = 1.846660838 + -3.1875 Combine like terms: 1.846660838 + -3.1875 = -1.340839162 x = -1.340839162 Simplifying x = -1.340839162Subproblem 2
x + 3.1875 = -1.846660838 Simplifying x + 3.1875 = -1.846660838 Reorder the terms: 3.1875 + x = -1.846660838 Solving 3.1875 + x = -1.846660838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.1875' to each side of the equation. 3.1875 + -3.1875 + x = -1.846660838 + -3.1875 Combine like terms: 3.1875 + -3.1875 = 0.0000 0.0000 + x = -1.846660838 + -3.1875 x = -1.846660838 + -3.1875 Combine like terms: -1.846660838 + -3.1875 = -5.034160838 x = -5.034160838 Simplifying x = -5.034160838Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.340839162, -5.034160838}
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