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Simplifying 8x2 + 43x + 5 = 0 Reorder the terms: 5 + 43x + 8x2 = 0 Solving 5 + 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'. 0.625 + 5.375x + x2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + 5.375x + -0.625 + x2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + 5.375x + x2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + 5.375x + x2 = 0 + -0.625 5.375x + x2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 5.375x + x2 = -0.625 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 = -0.625 + 7.22265625 Reorder the terms: 7.22265625 + 5.375x + x2 = -0.625 + 7.22265625 Combine like terms: -0.625 + 7.22265625 = 6.59765625 7.22265625 + 5.375x + x2 = 6.59765625 Factor a perfect square on the left side: (x + 2.6875)(x + 2.6875) = 6.59765625 Calculate the square root of the right side: 2.568590324 Break this problem into two subproblems by setting (x + 2.6875) equal to 2.568590324 and -2.568590324.Subproblem 1
x + 2.6875 = 2.568590324 Simplifying x + 2.6875 = 2.568590324 Reorder the terms: 2.6875 + x = 2.568590324 Solving 2.6875 + x = 2.568590324 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 = 2.568590324 + -2.6875 Combine like terms: 2.6875 + -2.6875 = 0.0000 0.0000 + x = 2.568590324 + -2.6875 x = 2.568590324 + -2.6875 Combine like terms: 2.568590324 + -2.6875 = -0.118909676 x = -0.118909676 Simplifying x = -0.118909676Subproblem 2
x + 2.6875 = -2.568590324 Simplifying x + 2.6875 = -2.568590324 Reorder the terms: 2.6875 + x = -2.568590324 Solving 2.6875 + x = -2.568590324 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 = -2.568590324 + -2.6875 Combine like terms: 2.6875 + -2.6875 = 0.0000 0.0000 + x = -2.568590324 + -2.6875 x = -2.568590324 + -2.6875 Combine like terms: -2.568590324 + -2.6875 = -5.256090324 x = -5.256090324 Simplifying x = -5.256090324Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.118909676, -5.256090324}
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