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Simplifying 8x2 + 8x + 1 = 46 Reorder the terms: 1 + 8x + 8x2 = 46 Solving 1 + 8x + 8x2 = 46 Solving for variable 'x'. Reorder the terms: 1 + -46 + 8x + 8x2 = 46 + -46 Combine like terms: 1 + -46 = -45 -45 + 8x + 8x2 = 46 + -46 Combine like terms: 46 + -46 = 0 -45 + 8x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -5.625 + x + x2 = 0 Move the constant term to the right: Add '5.625' to each side of the equation. -5.625 + x + 5.625 + x2 = 0 + 5.625 Reorder the terms: -5.625 + 5.625 + x + x2 = 0 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + x + x2 = 0 + 5.625 x + x2 = 0 + 5.625 Combine like terms: 0 + 5.625 = 5.625 x + x2 = 5.625 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 5.625 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 5.625 + 0.25 Combine like terms: 5.625 + 0.25 = 5.875 1.25 + x2 = 5.875 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 5.875 Calculate the square root of the right side: 2.423839929 Break this problem into two subproblems by setting (x + 0.5) equal to 2.423839929 and -2.423839929.Subproblem 1
x + 0.5 = 2.423839929 Simplifying x + 0.5 = 2.423839929 Reorder the terms: 0.5 + x = 2.423839929 Solving 0.5 + x = 2.423839929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.423839929 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.423839929 + -0.5 x = 2.423839929 + -0.5 Combine like terms: 2.423839929 + -0.5 = 1.923839929 x = 1.923839929 Simplifying x = 1.923839929Subproblem 2
x + 0.5 = -2.423839929 Simplifying x + 0.5 = -2.423839929 Reorder the terms: 0.5 + x = -2.423839929 Solving 0.5 + x = -2.423839929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.423839929 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.423839929 + -0.5 x = -2.423839929 + -0.5 Combine like terms: -2.423839929 + -0.5 = -2.923839929 x = -2.923839929 Simplifying x = -2.923839929Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.923839929, -2.923839929}
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