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Simplifying 8x2 + 16x + -51 = 0 Reorder the terms: -51 + 16x + 8x2 = 0 Solving -51 + 16x + 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'. -6.375 + 2x + x2 = 0 Move the constant term to the right: Add '6.375' to each side of the equation. -6.375 + 2x + 6.375 + x2 = 0 + 6.375 Reorder the terms: -6.375 + 6.375 + 2x + x2 = 0 + 6.375 Combine like terms: -6.375 + 6.375 = 0.000 0.000 + 2x + x2 = 0 + 6.375 2x + x2 = 0 + 6.375 Combine like terms: 0 + 6.375 = 6.375 2x + x2 = 6.375 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 6.375 + 1 Reorder the terms: 1 + 2x + x2 = 6.375 + 1 Combine like terms: 6.375 + 1 = 7.375 1 + 2x + x2 = 7.375 Factor a perfect square on the left side: (x + 1)(x + 1) = 7.375 Calculate the square root of the right side: 2.715695123 Break this problem into two subproblems by setting (x + 1) equal to 2.715695123 and -2.715695123.Subproblem 1
x + 1 = 2.715695123 Simplifying x + 1 = 2.715695123 Reorder the terms: 1 + x = 2.715695123 Solving 1 + x = 2.715695123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.715695123 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.715695123 + -1 x = 2.715695123 + -1 Combine like terms: 2.715695123 + -1 = 1.715695123 x = 1.715695123 Simplifying x = 1.715695123Subproblem 2
x + 1 = -2.715695123 Simplifying x + 1 = -2.715695123 Reorder the terms: 1 + x = -2.715695123 Solving 1 + x = -2.715695123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.715695123 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.715695123 + -1 x = -2.715695123 + -1 Combine like terms: -2.715695123 + -1 = -3.715695123 x = -3.715695123 Simplifying x = -3.715695123Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.715695123, -3.715695123}
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