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Simplifying (2x + -11)(2x + 5) = 64 Reorder the terms: (-11 + 2x)(2x + 5) = 64 Reorder the terms: (-11 + 2x)(5 + 2x) = 64 Multiply (-11 + 2x) * (5 + 2x) (-11(5 + 2x) + 2x * (5 + 2x)) = 64 ((5 * -11 + 2x * -11) + 2x * (5 + 2x)) = 64 ((-55 + -22x) + 2x * (5 + 2x)) = 64 (-55 + -22x + (5 * 2x + 2x * 2x)) = 64 (-55 + -22x + (10x + 4x2)) = 64 Combine like terms: -22x + 10x = -12x (-55 + -12x + 4x2) = 64 Solving -55 + -12x + 4x2 = 64 Solving for variable 'x'. Reorder the terms: -55 + -64 + -12x + 4x2 = 64 + -64 Combine like terms: -55 + -64 = -119 -119 + -12x + 4x2 = 64 + -64 Combine like terms: 64 + -64 = 0 -119 + -12x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -29.75 + -3x + x2 = 0 Move the constant term to the right: Add '29.75' to each side of the equation. -29.75 + -3x + 29.75 + x2 = 0 + 29.75 Reorder the terms: -29.75 + 29.75 + -3x + x2 = 0 + 29.75 Combine like terms: -29.75 + 29.75 = 0.00 0.00 + -3x + x2 = 0 + 29.75 -3x + x2 = 0 + 29.75 Combine like terms: 0 + 29.75 = 29.75 -3x + x2 = 29.75 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 = 29.75 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 29.75 + 2.25 Combine like terms: 29.75 + 2.25 = 32 2.25 + -3x + x2 = 32 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x + -1.5) equal to 5.656854249 and -5.656854249.Subproblem 1
x + -1.5 = 5.656854249 Simplifying x + -1.5 = 5.656854249 Reorder the terms: -1.5 + x = 5.656854249 Solving -1.5 + x = 5.656854249 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 = 5.656854249 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 5.656854249 + 1.5 x = 5.656854249 + 1.5 Combine like terms: 5.656854249 + 1.5 = 7.156854249 x = 7.156854249 Simplifying x = 7.156854249Subproblem 2
x + -1.5 = -5.656854249 Simplifying x + -1.5 = -5.656854249 Reorder the terms: -1.5 + x = -5.656854249 Solving -1.5 + x = -5.656854249 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 = -5.656854249 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -5.656854249 + 1.5 x = -5.656854249 + 1.5 Combine like terms: -5.656854249 + 1.5 = -4.156854249 x = -4.156854249 Simplifying x = -4.156854249Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.156854249, -4.156854249}
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