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Simplifying (2x + 10)(2x + 5) = 54 Reorder the terms: (10 + 2x)(2x + 5) = 54 Reorder the terms: (10 + 2x)(5 + 2x) = 54 Multiply (10 + 2x) * (5 + 2x) (10(5 + 2x) + 2x * (5 + 2x)) = 54 ((5 * 10 + 2x * 10) + 2x * (5 + 2x)) = 54 ((50 + 20x) + 2x * (5 + 2x)) = 54 (50 + 20x + (5 * 2x + 2x * 2x)) = 54 (50 + 20x + (10x + 4x2)) = 54 Combine like terms: 20x + 10x = 30x (50 + 30x + 4x2) = 54 Solving 50 + 30x + 4x2 = 54 Solving for variable 'x'. Reorder the terms: 50 + -54 + 30x + 4x2 = 54 + -54 Combine like terms: 50 + -54 = -4 -4 + 30x + 4x2 = 54 + -54 Combine like terms: 54 + -54 = 0 -4 + 30x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 15x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 15x + 2x2)' equal to zero and attempt to solve: Simplifying -2 + 15x + 2x2 = 0 Solving -2 + 15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1 + 7.5x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 7.5x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 7.5x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 7.5x + x2 = 0 + 1 7.5x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 7.5x + x2 = 1 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 = 1 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 1 + 14.0625 Combine like terms: 1 + 14.0625 = 15.0625 14.0625 + 7.5x + x2 = 15.0625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 15.0625 Calculate the square root of the right side: 3.881043674 Break this problem into two subproblems by setting (x + 3.75) equal to 3.881043674 and -3.881043674.Subproblem 1
x + 3.75 = 3.881043674 Simplifying x + 3.75 = 3.881043674 Reorder the terms: 3.75 + x = 3.881043674 Solving 3.75 + x = 3.881043674 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 = 3.881043674 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 3.881043674 + -3.75 x = 3.881043674 + -3.75 Combine like terms: 3.881043674 + -3.75 = 0.131043674 x = 0.131043674 Simplifying x = 0.131043674Subproblem 2
x + 3.75 = -3.881043674 Simplifying x + 3.75 = -3.881043674 Reorder the terms: 3.75 + x = -3.881043674 Solving 3.75 + x = -3.881043674 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 = -3.881043674 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -3.881043674 + -3.75 x = -3.881043674 + -3.75 Combine like terms: -3.881043674 + -3.75 = -7.631043674 x = -7.631043674 Simplifying x = -7.631043674Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.131043674, -7.631043674}Solution
x = {0.131043674, -7.631043674}
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