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Simplifying 8x2 + 8x = 17 Reorder the terms: 8x + 8x2 = 17 Solving 8x + 8x2 = 17 Solving for variable 'x'. Reorder the terms: -17 + 8x + 8x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + 8x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.125 + x + x2 = 0 Move the constant term to the right: Add '2.125' to each side of the equation. -2.125 + x + 2.125 + x2 = 0 + 2.125 Reorder the terms: -2.125 + 2.125 + x + x2 = 0 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x + x2 = 0 + 2.125 x + x2 = 0 + 2.125 Combine like terms: 0 + 2.125 = 2.125 x + x2 = 2.125 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 = 2.125 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 2.125 + 0.25 Combine like terms: 2.125 + 0.25 = 2.375 1.25 + x2 = 2.375 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.375 Calculate the square root of the right side: 1.541103501 Break this problem into two subproblems by setting (x + 0.5) equal to 1.541103501 and -1.541103501.Subproblem 1
x + 0.5 = 1.541103501 Simplifying x + 0.5 = 1.541103501 Reorder the terms: 0.5 + x = 1.541103501 Solving 0.5 + x = 1.541103501 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 = 1.541103501 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.541103501 + -0.5 x = 1.541103501 + -0.5 Combine like terms: 1.541103501 + -0.5 = 1.041103501 x = 1.041103501 Simplifying x = 1.041103501Subproblem 2
x + 0.5 = -1.541103501 Simplifying x + 0.5 = -1.541103501 Reorder the terms: 0.5 + x = -1.541103501 Solving 0.5 + x = -1.541103501 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 = -1.541103501 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.541103501 + -0.5 x = -1.541103501 + -0.5 Combine like terms: -1.541103501 + -0.5 = -2.041103501 x = -2.041103501 Simplifying x = -2.041103501Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.041103501, -2.041103501}
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