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Simplifying 8x2 + 5x = 23 Reorder the terms: 5x + 8x2 = 23 Solving 5x + 8x2 = 23 Solving for variable 'x'. Reorder the terms: -23 + 5x + 8x2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + 5x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.875 + 0.625x + x2 = 0 Move the constant term to the right: Add '2.875' to each side of the equation. -2.875 + 0.625x + 2.875 + x2 = 0 + 2.875 Reorder the terms: -2.875 + 2.875 + 0.625x + x2 = 0 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + 0.625x + x2 = 0 + 2.875 0.625x + x2 = 0 + 2.875 Combine like terms: 0 + 2.875 = 2.875 0.625x + x2 = 2.875 The x term is 0.625x. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625x + 0.09765625 + x2 = 2.875 + 0.09765625 Reorder the terms: 0.09765625 + 0.625x + x2 = 2.875 + 0.09765625 Combine like terms: 2.875 + 0.09765625 = 2.97265625 0.09765625 + 0.625x + x2 = 2.97265625 Factor a perfect square on the left side: (x + 0.3125)(x + 0.3125) = 2.97265625 Calculate the square root of the right side: 1.724139278 Break this problem into two subproblems by setting (x + 0.3125) equal to 1.724139278 and -1.724139278.Subproblem 1
x + 0.3125 = 1.724139278 Simplifying x + 0.3125 = 1.724139278 Reorder the terms: 0.3125 + x = 1.724139278 Solving 0.3125 + x = 1.724139278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x = 1.724139278 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = 1.724139278 + -0.3125 x = 1.724139278 + -0.3125 Combine like terms: 1.724139278 + -0.3125 = 1.411639278 x = 1.411639278 Simplifying x = 1.411639278Subproblem 2
x + 0.3125 = -1.724139278 Simplifying x + 0.3125 = -1.724139278 Reorder the terms: 0.3125 + x = -1.724139278 Solving 0.3125 + x = -1.724139278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x = -1.724139278 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = -1.724139278 + -0.3125 x = -1.724139278 + -0.3125 Combine like terms: -1.724139278 + -0.3125 = -2.036639278 x = -2.036639278 Simplifying x = -2.036639278Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.411639278, -2.036639278}
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