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Simplifying 2 = 5(x + 9) * 8x Reorder the terms: 2 = 5(9 + x) * 8x Reorder the terms for easier multiplication: 2 = 5 * 8x(9 + x) Multiply 5 * 8 2 = 40x(9 + x) 2 = (9 * 40x + x * 40x) 2 = (360x + 40x2) Solving 2 = 360x + 40x2 Solving for variable 'x'. Reorder the terms: 2 + -360x + -40x2 = 360x + -360x + 40x2 + -40x2 Combine like terms: 360x + -360x = 0 2 + -360x + -40x2 = 0 + 40x2 + -40x2 2 + -360x + -40x2 = 40x2 + -40x2 Combine like terms: 40x2 + -40x2 = 0 2 + -360x + -40x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -180x + -20x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -180x + -20x2)' equal to zero and attempt to solve: Simplifying 1 + -180x + -20x2 = 0 Solving 1 + -180x + -20x2 = 0 Begin completing the square. Divide all terms by -20 the coefficient of the squared term: Divide each side by '-20'. -0.05 + 9x + x2 = 0.0 Move the constant term to the right: Add '0.05' to each side of the equation. -0.05 + 9x + 0.05 + x2 = 0.0 + 0.05 Reorder the terms: -0.05 + 0.05 + 9x + x2 = 0.0 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + 9x + x2 = 0.0 + 0.05 9x + x2 = 0.0 + 0.05 Combine like terms: 0.0 + 0.05 = 0.05 9x + x2 = 0.05 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 0.05 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 0.05 + 20.25 Combine like terms: 0.05 + 20.25 = 20.3 20.25 + 9x + x2 = 20.3 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 20.3 Calculate the square root of the right side: 4.50555213 Break this problem into two subproblems by setting (x + 4.5) equal to 4.50555213 and -4.50555213.Subproblem 1
x + 4.5 = 4.50555213 Simplifying x + 4.5 = 4.50555213 Reorder the terms: 4.5 + x = 4.50555213 Solving 4.5 + x = 4.50555213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 4.50555213 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 4.50555213 + -4.5 x = 4.50555213 + -4.5 Combine like terms: 4.50555213 + -4.5 = 0.00555213 x = 0.00555213 Simplifying x = 0.00555213Subproblem 2
x + 4.5 = -4.50555213 Simplifying x + 4.5 = -4.50555213 Reorder the terms: 4.5 + x = -4.50555213 Solving 4.5 + x = -4.50555213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -4.50555213 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -4.50555213 + -4.5 x = -4.50555213 + -4.5 Combine like terms: -4.50555213 + -4.5 = -9.00555213 x = -9.00555213 Simplifying x = -9.00555213Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.00555213, -9.00555213}Solution
x = {0.00555213, -9.00555213}
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