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Simplifying (5)(x + 3)(x + 3) = 90 Reorder the terms: 5(3 + x)(x + 3) = 90 Reorder the terms: 5(3 + x)(3 + x) = 90 Multiply (3 + x) * (3 + x) 5(3(3 + x) + x(3 + x)) = 90 5((3 * 3 + x * 3) + x(3 + x)) = 90 5((9 + 3x) + x(3 + x)) = 90 5(9 + 3x + (3 * x + x * x)) = 90 5(9 + 3x + (3x + x2)) = 90 Combine like terms: 3x + 3x = 6x 5(9 + 6x + x2) = 90 (9 * 5 + 6x * 5 + x2 * 5) = 90 (45 + 30x + 5x2) = 90 Solving 45 + 30x + 5x2 = 90 Solving for variable 'x'. Reorder the terms: 45 + -90 + 30x + 5x2 = 90 + -90 Combine like terms: 45 + -90 = -45 -45 + 30x + 5x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -45 + 30x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-9 + 6x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-9 + 6x + x2)' equal to zero and attempt to solve: Simplifying -9 + 6x + x2 = 0 Solving -9 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 6x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 6x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 6x + x2 = 0 + 9 6x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 6x + x2 = 9 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 9 + 9 Reorder the terms: 9 + 6x + x2 = 9 + 9 Combine like terms: 9 + 9 = 18 9 + 6x + x2 = 18 Factor a perfect square on the left side: (x + 3)(x + 3) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x + 3) equal to 4.242640687 and -4.242640687.Subproblem 1
x + 3 = 4.242640687 Simplifying x + 3 = 4.242640687 Reorder the terms: 3 + x = 4.242640687 Solving 3 + x = 4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 4.242640687 + -3 Combine like terms: 3 + -3 = 0 0 + x = 4.242640687 + -3 x = 4.242640687 + -3 Combine like terms: 4.242640687 + -3 = 1.242640687 x = 1.242640687 Simplifying x = 1.242640687Subproblem 2
x + 3 = -4.242640687 Simplifying x + 3 = -4.242640687 Reorder the terms: 3 + x = -4.242640687 Solving 3 + x = -4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -4.242640687 + -3 Combine like terms: 3 + -3 = 0 0 + x = -4.242640687 + -3 x = -4.242640687 + -3 Combine like terms: -4.242640687 + -3 = -7.242640687 x = -7.242640687 Simplifying x = -7.242640687Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.242640687, -7.242640687}Solution
x = {1.242640687, -7.242640687}
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