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Simplifying 4x(2x + 3) = 11 Reorder the terms: 4x(3 + 2x) = 11 (3 * 4x + 2x * 4x) = 11 (12x + 8x2) = 11 Solving 12x + 8x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + 12x + 8x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 12x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.375 + 1.5x + x2 = 0 Move the constant term to the right: Add '1.375' to each side of the equation. -1.375 + 1.5x + 1.375 + x2 = 0 + 1.375 Reorder the terms: -1.375 + 1.375 + 1.5x + x2 = 0 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + 1.5x + x2 = 0 + 1.375 1.5x + x2 = 0 + 1.375 Combine like terms: 0 + 1.375 = 1.375 1.5x + x2 = 1.375 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 1.375 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 1.375 + 0.5625 Combine like terms: 1.375 + 0.5625 = 1.9375 0.5625 + 1.5x + x2 = 1.9375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 1.9375 Calculate the square root of the right side: 1.391941091 Break this problem into two subproblems by setting (x + 0.75) equal to 1.391941091 and -1.391941091.Subproblem 1
x + 0.75 = 1.391941091 Simplifying x + 0.75 = 1.391941091 Reorder the terms: 0.75 + x = 1.391941091 Solving 0.75 + x = 1.391941091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 1.391941091 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 1.391941091 + -0.75 x = 1.391941091 + -0.75 Combine like terms: 1.391941091 + -0.75 = 0.641941091 x = 0.641941091 Simplifying x = 0.641941091Subproblem 2
x + 0.75 = -1.391941091 Simplifying x + 0.75 = -1.391941091 Reorder the terms: 0.75 + x = -1.391941091 Solving 0.75 + x = -1.391941091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -1.391941091 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -1.391941091 + -0.75 x = -1.391941091 + -0.75 Combine like terms: -1.391941091 + -0.75 = -2.141941091 x = -2.141941091 Simplifying x = -2.141941091Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.641941091, -2.141941091}
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