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Simplifying (10 + 2x)(5 + 2x) = 2916 Multiply (10 + 2x) * (5 + 2x) (10(5 + 2x) + 2x * (5 + 2x)) = 2916 ((5 * 10 + 2x * 10) + 2x * (5 + 2x)) = 2916 ((50 + 20x) + 2x * (5 + 2x)) = 2916 (50 + 20x + (5 * 2x + 2x * 2x)) = 2916 (50 + 20x + (10x + 4x2)) = 2916 Combine like terms: 20x + 10x = 30x (50 + 30x + 4x2) = 2916 Solving 50 + 30x + 4x2 = 2916 Solving for variable 'x'. Reorder the terms: 50 + -2916 + 30x + 4x2 = 2916 + -2916 Combine like terms: 50 + -2916 = -2866 -2866 + 30x + 4x2 = 2916 + -2916 Combine like terms: 2916 + -2916 = 0 -2866 + 30x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1433 + 15x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1433 + 15x + 2x2)' equal to zero and attempt to solve: Simplifying -1433 + 15x + 2x2 = 0 Solving -1433 + 15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -716.5 + 7.5x + x2 = 0 Move the constant term to the right: Add '716.5' to each side of the equation. -716.5 + 7.5x + 716.5 + x2 = 0 + 716.5 Reorder the terms: -716.5 + 716.5 + 7.5x + x2 = 0 + 716.5 Combine like terms: -716.5 + 716.5 = 0.0 0.0 + 7.5x + x2 = 0 + 716.5 7.5x + x2 = 0 + 716.5 Combine like terms: 0 + 716.5 = 716.5 7.5x + x2 = 716.5 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = 716.5 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 716.5 + 14.0625 Combine like terms: 716.5 + 14.0625 = 730.5625 14.0625 + 7.5x + x2 = 730.5625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 730.5625 Calculate the square root of the right side: 27.028919697 Break this problem into two subproblems by setting (x + 3.75) equal to 27.028919697 and -27.028919697.Subproblem 1
x + 3.75 = 27.028919697 Simplifying x + 3.75 = 27.028919697 Reorder the terms: 3.75 + x = 27.028919697 Solving 3.75 + x = 27.028919697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 27.028919697 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 27.028919697 + -3.75 x = 27.028919697 + -3.75 Combine like terms: 27.028919697 + -3.75 = 23.278919697 x = 23.278919697 Simplifying x = 23.278919697Subproblem 2
x + 3.75 = -27.028919697 Simplifying x + 3.75 = -27.028919697 Reorder the terms: 3.75 + x = -27.028919697 Solving 3.75 + x = -27.028919697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -27.028919697 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -27.028919697 + -3.75 x = -27.028919697 + -3.75 Combine like terms: -27.028919697 + -3.75 = -30.778919697 x = -30.778919697 Simplifying x = -30.778919697Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.278919697, -30.778919697}Solution
x = {23.278919697, -30.778919697}
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