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Simplifying 8x2 + 23x = 298 Reorder the terms: 23x + 8x2 = 298 Solving 23x + 8x2 = 298 Solving for variable 'x'. Reorder the terms: -298 + 23x + 8x2 = 298 + -298 Combine like terms: 298 + -298 = 0 -298 + 23x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -37.25 + 2.875x + x2 = 0 Move the constant term to the right: Add '37.25' to each side of the equation. -37.25 + 2.875x + 37.25 + x2 = 0 + 37.25 Reorder the terms: -37.25 + 37.25 + 2.875x + x2 = 0 + 37.25 Combine like terms: -37.25 + 37.25 = 0.00 0.00 + 2.875x + x2 = 0 + 37.25 2.875x + x2 = 0 + 37.25 Combine like terms: 0 + 37.25 = 37.25 2.875x + x2 = 37.25 The x term is 2.875x. Take half its coefficient (1.4375). Square it (2.06640625) and add it to both sides. Add '2.06640625' to each side of the equation. 2.875x + 2.06640625 + x2 = 37.25 + 2.06640625 Reorder the terms: 2.06640625 + 2.875x + x2 = 37.25 + 2.06640625 Combine like terms: 37.25 + 2.06640625 = 39.31640625 2.06640625 + 2.875x + x2 = 39.31640625 Factor a perfect square on the left side: (x + 1.4375)(x + 1.4375) = 39.31640625 Calculate the square root of the right side: 6.270279599 Break this problem into two subproblems by setting (x + 1.4375) equal to 6.270279599 and -6.270279599.Subproblem 1
x + 1.4375 = 6.270279599 Simplifying x + 1.4375 = 6.270279599 Reorder the terms: 1.4375 + x = 6.270279599 Solving 1.4375 + x = 6.270279599 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4375' to each side of the equation. 1.4375 + -1.4375 + x = 6.270279599 + -1.4375 Combine like terms: 1.4375 + -1.4375 = 0.0000 0.0000 + x = 6.270279599 + -1.4375 x = 6.270279599 + -1.4375 Combine like terms: 6.270279599 + -1.4375 = 4.832779599 x = 4.832779599 Simplifying x = 4.832779599Subproblem 2
x + 1.4375 = -6.270279599 Simplifying x + 1.4375 = -6.270279599 Reorder the terms: 1.4375 + x = -6.270279599 Solving 1.4375 + x = -6.270279599 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4375' to each side of the equation. 1.4375 + -1.4375 + x = -6.270279599 + -1.4375 Combine like terms: 1.4375 + -1.4375 = 0.0000 0.0000 + x = -6.270279599 + -1.4375 x = -6.270279599 + -1.4375 Combine like terms: -6.270279599 + -1.4375 = -7.707779599 x = -7.707779599 Simplifying x = -7.707779599Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.832779599, -7.707779599}
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