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Simplifying 8x2 + 21 = 39x Reorder the terms: 21 + 8x2 = 39x Solving 21 + 8x2 = 39x Solving for variable 'x'. Reorder the terms: 21 + -39x + 8x2 = 39x + -39x Combine like terms: 39x + -39x = 0 21 + -39x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 2.625 + -4.875x + x2 = 0 Move the constant term to the right: Add '-2.625' to each side of the equation. 2.625 + -4.875x + -2.625 + x2 = 0 + -2.625 Reorder the terms: 2.625 + -2.625 + -4.875x + x2 = 0 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + -4.875x + x2 = 0 + -2.625 -4.875x + x2 = 0 + -2.625 Combine like terms: 0 + -2.625 = -2.625 -4.875x + x2 = -2.625 The x term is -4.875x. Take half its coefficient (-2.4375). Square it (5.94140625) and add it to both sides. Add '5.94140625' to each side of the equation. -4.875x + 5.94140625 + x2 = -2.625 + 5.94140625 Reorder the terms: 5.94140625 + -4.875x + x2 = -2.625 + 5.94140625 Combine like terms: -2.625 + 5.94140625 = 3.31640625 5.94140625 + -4.875x + x2 = 3.31640625 Factor a perfect square on the left side: (x + -2.4375)(x + -2.4375) = 3.31640625 Calculate the square root of the right side: 1.821100286 Break this problem into two subproblems by setting (x + -2.4375) equal to 1.821100286 and -1.821100286.Subproblem 1
x + -2.4375 = 1.821100286 Simplifying x + -2.4375 = 1.821100286 Reorder the terms: -2.4375 + x = 1.821100286 Solving -2.4375 + x = 1.821100286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4375' to each side of the equation. -2.4375 + 2.4375 + x = 1.821100286 + 2.4375 Combine like terms: -2.4375 + 2.4375 = 0.0000 0.0000 + x = 1.821100286 + 2.4375 x = 1.821100286 + 2.4375 Combine like terms: 1.821100286 + 2.4375 = 4.258600286 x = 4.258600286 Simplifying x = 4.258600286Subproblem 2
x + -2.4375 = -1.821100286 Simplifying x + -2.4375 = -1.821100286 Reorder the terms: -2.4375 + x = -1.821100286 Solving -2.4375 + x = -1.821100286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4375' to each side of the equation. -2.4375 + 2.4375 + x = -1.821100286 + 2.4375 Combine like terms: -2.4375 + 2.4375 = 0.0000 0.0000 + x = -1.821100286 + 2.4375 x = -1.821100286 + 2.4375 Combine like terms: -1.821100286 + 2.4375 = 0.616399714 x = 0.616399714 Simplifying x = 0.616399714Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.258600286, 0.616399714}
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