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Simplifying 8x2 + 43x + 30 = 0 Reorder the terms: 30 + 43x + 8x2 = 0 Solving 30 + 43x + 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'. 3.75 + 5.375x + x2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + 5.375x + -3.75 + x2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + 5.375x + x2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + 5.375x + x2 = 0 + -3.75 5.375x + x2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 5.375x + x2 = -3.75 The x term is 5.375x. Take half its coefficient (2.6875). Square it (7.22265625) and add it to both sides. Add '7.22265625' to each side of the equation. 5.375x + 7.22265625 + x2 = -3.75 + 7.22265625 Reorder the terms: 7.22265625 + 5.375x + x2 = -3.75 + 7.22265625 Combine like terms: -3.75 + 7.22265625 = 3.47265625 7.22265625 + 5.375x + x2 = 3.47265625 Factor a perfect square on the left side: (x + 2.6875)(x + 2.6875) = 3.47265625 Calculate the square root of the right side: 1.863506439 Break this problem into two subproblems by setting (x + 2.6875) equal to 1.863506439 and -1.863506439.Subproblem 1
x + 2.6875 = 1.863506439 Simplifying x + 2.6875 = 1.863506439 Reorder the terms: 2.6875 + x = 1.863506439 Solving 2.6875 + x = 1.863506439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6875' to each side of the equation. 2.6875 + -2.6875 + x = 1.863506439 + -2.6875 Combine like terms: 2.6875 + -2.6875 = 0.0000 0.0000 + x = 1.863506439 + -2.6875 x = 1.863506439 + -2.6875 Combine like terms: 1.863506439 + -2.6875 = -0.823993561 x = -0.823993561 Simplifying x = -0.823993561Subproblem 2
x + 2.6875 = -1.863506439 Simplifying x + 2.6875 = -1.863506439 Reorder the terms: 2.6875 + x = -1.863506439 Solving 2.6875 + x = -1.863506439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6875' to each side of the equation. 2.6875 + -2.6875 + x = -1.863506439 + -2.6875 Combine like terms: 2.6875 + -2.6875 = 0.0000 0.0000 + x = -1.863506439 + -2.6875 x = -1.863506439 + -2.6875 Combine like terms: -1.863506439 + -2.6875 = -4.551006439 x = -4.551006439 Simplifying x = -4.551006439Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.823993561, -4.551006439}
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