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Simplifying 8x(x + 3) = 11 Reorder the terms: 8x(3 + x) = 11 (3 * 8x + x * 8x) = 11 (24x + 8x2) = 11 Solving 24x + 8x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + 24x + 8x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 24x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.375 + 3x + x2 = 0 Move the constant term to the right: Add '1.375' to each side of the equation. -1.375 + 3x + 1.375 + x2 = 0 + 1.375 Reorder the terms: -1.375 + 1.375 + 3x + x2 = 0 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + 3x + x2 = 0 + 1.375 3x + x2 = 0 + 1.375 Combine like terms: 0 + 1.375 = 1.375 3x + x2 = 1.375 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 1.375 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 1.375 + 2.25 Combine like terms: 1.375 + 2.25 = 3.625 2.25 + 3x + x2 = 3.625 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 3.625 Calculate the square root of the right side: 1.903943276 Break this problem into two subproblems by setting (x + 1.5) equal to 1.903943276 and -1.903943276.Subproblem 1
x + 1.5 = 1.903943276 Simplifying x + 1.5 = 1.903943276 Reorder the terms: 1.5 + x = 1.903943276 Solving 1.5 + x = 1.903943276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.903943276 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.903943276 + -1.5 x = 1.903943276 + -1.5 Combine like terms: 1.903943276 + -1.5 = 0.403943276 x = 0.403943276 Simplifying x = 0.403943276Subproblem 2
x + 1.5 = -1.903943276 Simplifying x + 1.5 = -1.903943276 Reorder the terms: 1.5 + x = -1.903943276 Solving 1.5 + x = -1.903943276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.903943276 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.903943276 + -1.5 x = -1.903943276 + -1.5 Combine like terms: -1.903943276 + -1.5 = -3.403943276 x = -3.403943276 Simplifying x = -3.403943276Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.403943276, -3.403943276}
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