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Simplifying 3(2x + 5)(2x + 5) = 90 Reorder the terms: 3(5 + 2x)(2x + 5) = 90 Reorder the terms: 3(5 + 2x)(5 + 2x) = 90 Multiply (5 + 2x) * (5 + 2x) 3(5(5 + 2x) + 2x * (5 + 2x)) = 90 3((5 * 5 + 2x * 5) + 2x * (5 + 2x)) = 90 3((25 + 10x) + 2x * (5 + 2x)) = 90 3(25 + 10x + (5 * 2x + 2x * 2x)) = 90 3(25 + 10x + (10x + 4x2)) = 90 Combine like terms: 10x + 10x = 20x 3(25 + 20x + 4x2) = 90 (25 * 3 + 20x * 3 + 4x2 * 3) = 90 (75 + 60x + 12x2) = 90 Solving 75 + 60x + 12x2 = 90 Solving for variable 'x'. Reorder the terms: 75 + -90 + 60x + 12x2 = 90 + -90 Combine like terms: 75 + -90 = -15 -15 + 60x + 12x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -15 + 60x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 20x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + 20x + 4x2)' equal to zero and attempt to solve: Simplifying -5 + 20x + 4x2 = 0 Solving -5 + 20x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + 5x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 5x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 5x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 5x + x2 = 0 + 1.25 5x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 5x + x2 = 1.25 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 1.25 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 1.25 + 6.25 Combine like terms: 1.25 + 6.25 = 7.5 6.25 + 5x + x2 = 7.5 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 7.5 Calculate the square root of the right side: 2.738612788 Break this problem into two subproblems by setting (x + 2.5) equal to 2.738612788 and -2.738612788.Subproblem 1
x + 2.5 = 2.738612788 Simplifying x + 2.5 = 2.738612788 Reorder the terms: 2.5 + x = 2.738612788 Solving 2.5 + x = 2.738612788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.738612788 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.738612788 + -2.5 x = 2.738612788 + -2.5 Combine like terms: 2.738612788 + -2.5 = 0.238612788 x = 0.238612788 Simplifying x = 0.238612788Subproblem 2
x + 2.5 = -2.738612788 Simplifying x + 2.5 = -2.738612788 Reorder the terms: 2.5 + x = -2.738612788 Solving 2.5 + x = -2.738612788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.738612788 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.738612788 + -2.5 x = -2.738612788 + -2.5 Combine like terms: -2.738612788 + -2.5 = -5.238612788 x = -5.238612788 Simplifying x = -5.238612788Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.238612788, -5.238612788}Solution
x = {0.238612788, -5.238612788}
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