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Simplifying 9x(5x + 5) = 27 Reorder the terms: 9x(5 + 5x) = 27 (5 * 9x + 5x * 9x) = 27 (45x + 45x2) = 27 Solving 45x + 45x2 = 27 Solving for variable 'x'. Reorder the terms: -27 + 45x + 45x2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + 45x + 45x2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(-3 + 5x + 5x2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(-3 + 5x + 5x2)' equal to zero and attempt to solve: Simplifying -3 + 5x + 5x2 = 0 Solving -3 + 5x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x + x2 = 0 + 0.6 x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 x + x2 = 0.6 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 0.6 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.6 + 0.25 Combine like terms: 0.6 + 0.25 = 0.85 1.25 + x2 = 0.85 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.85 Calculate the square root of the right side: 0.921954446 Break this problem into two subproblems by setting (x + 0.5) equal to 0.921954446 and -0.921954446.Subproblem 1
x + 0.5 = 0.921954446 Simplifying x + 0.5 = 0.921954446 Reorder the terms: 0.5 + x = 0.921954446 Solving 0.5 + x = 0.921954446 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.921954446 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.921954446 + -0.5 x = 0.921954446 + -0.5 Combine like terms: 0.921954446 + -0.5 = 0.421954446 x = 0.421954446 Simplifying x = 0.421954446Subproblem 2
x + 0.5 = -0.921954446 Simplifying x + 0.5 = -0.921954446 Reorder the terms: 0.5 + x = -0.921954446 Solving 0.5 + x = -0.921954446 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.921954446 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.921954446 + -0.5 x = -0.921954446 + -0.5 Combine like terms: -0.921954446 + -0.5 = -1.421954446 x = -1.421954446 Simplifying x = -1.421954446Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.421954446, -1.421954446}Solution
x = {0.421954446, -1.421954446}
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