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Simplifying 8x2 + 51x + -13 = 0 Reorder the terms: -13 + 51x + 8x2 = 0 Solving -13 + 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'. -1.625 + 6.375x + x2 = 0 Move the constant term to the right: Add '1.625' to each side of the equation. -1.625 + 6.375x + 1.625 + x2 = 0 + 1.625 Reorder the terms: -1.625 + 1.625 + 6.375x + x2 = 0 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + 6.375x + x2 = 0 + 1.625 6.375x + x2 = 0 + 1.625 Combine like terms: 0 + 1.625 = 1.625 6.375x + x2 = 1.625 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 = 1.625 + 10.16015625 Reorder the terms: 10.16015625 + 6.375x + x2 = 1.625 + 10.16015625 Combine like terms: 1.625 + 10.16015625 = 11.78515625 10.16015625 + 6.375x + x2 = 11.78515625 Factor a perfect square on the left side: (x + 3.1875)(x + 3.1875) = 11.78515625 Calculate the square root of the right side: 3.432951536 Break this problem into two subproblems by setting (x + 3.1875) equal to 3.432951536 and -3.432951536.Subproblem 1
x + 3.1875 = 3.432951536 Simplifying x + 3.1875 = 3.432951536 Reorder the terms: 3.1875 + x = 3.432951536 Solving 3.1875 + x = 3.432951536 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 = 3.432951536 + -3.1875 Combine like terms: 3.1875 + -3.1875 = 0.0000 0.0000 + x = 3.432951536 + -3.1875 x = 3.432951536 + -3.1875 Combine like terms: 3.432951536 + -3.1875 = 0.245451536 x = 0.245451536 Simplifying x = 0.245451536Subproblem 2
x + 3.1875 = -3.432951536 Simplifying x + 3.1875 = -3.432951536 Reorder the terms: 3.1875 + x = -3.432951536 Solving 3.1875 + x = -3.432951536 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 = -3.432951536 + -3.1875 Combine like terms: 3.1875 + -3.1875 = 0.0000 0.0000 + x = -3.432951536 + -3.1875 x = -3.432951536 + -3.1875 Combine like terms: -3.432951536 + -3.1875 = -6.620451536 x = -6.620451536 Simplifying x = -6.620451536Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.245451536, -6.620451536}
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