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Simplifying 8x2 + -43x + -21 = 0 Reorder the terms: -21 + -43x + 8x2 = 0 Solving -21 + -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'. -2.625 + -5.375x + x2 = 0 Move the constant term to the right: Add '2.625' to each side of the equation. -2.625 + -5.375x + 2.625 + x2 = 0 + 2.625 Reorder the terms: -2.625 + 2.625 + -5.375x + x2 = 0 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + -5.375x + x2 = 0 + 2.625 -5.375x + x2 = 0 + 2.625 Combine like terms: 0 + 2.625 = 2.625 -5.375x + x2 = 2.625 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 = 2.625 + 7.22265625 Reorder the terms: 7.22265625 + -5.375x + x2 = 2.625 + 7.22265625 Combine like terms: 2.625 + 7.22265625 = 9.84765625 7.22265625 + -5.375x + x2 = 9.84765625 Factor a perfect square on the left side: (x + -2.6875)(x + -2.6875) = 9.84765625 Calculate the square root of the right side: 3.138097553 Break this problem into two subproblems by setting (x + -2.6875) equal to 3.138097553 and -3.138097553.Subproblem 1
x + -2.6875 = 3.138097553 Simplifying x + -2.6875 = 3.138097553 Reorder the terms: -2.6875 + x = 3.138097553 Solving -2.6875 + x = 3.138097553 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 = 3.138097553 + 2.6875 Combine like terms: -2.6875 + 2.6875 = 0.0000 0.0000 + x = 3.138097553 + 2.6875 x = 3.138097553 + 2.6875 Combine like terms: 3.138097553 + 2.6875 = 5.825597553 x = 5.825597553 Simplifying x = 5.825597553Subproblem 2
x + -2.6875 = -3.138097553 Simplifying x + -2.6875 = -3.138097553 Reorder the terms: -2.6875 + x = -3.138097553 Solving -2.6875 + x = -3.138097553 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 = -3.138097553 + 2.6875 Combine like terms: -2.6875 + 2.6875 = 0.0000 0.0000 + x = -3.138097553 + 2.6875 x = -3.138097553 + 2.6875 Combine like terms: -3.138097553 + 2.6875 = -0.450597553 x = -0.450597553 Simplifying x = -0.450597553Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.825597553, -0.450597553}
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