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Simplifying 15x2 + 27x = 9 Reorder the terms: 27x + 15x2 = 9 Solving 27x + 15x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + 27x + 15x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 27x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + 9x + 5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + 9x + 5x2)' equal to zero and attempt to solve: Simplifying -3 + 9x + 5x2 = 0 Solving -3 + 9x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + 1.8x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 1.8x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 1.8x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 1.8x + x2 = 0 + 0.6 1.8x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 1.8x + x2 = 0.6 The x term is 1.8x. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8x + 0.81 + x2 = 0.6 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 0.6 + 0.81 Combine like terms: 0.6 + 0.81 = 1.41 0.81 + 1.8x + x2 = 1.41 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 1.41 Calculate the square root of the right side: 1.187434209 Break this problem into two subproblems by setting (x + 0.9) equal to 1.187434209 and -1.187434209.Subproblem 1
x + 0.9 = 1.187434209 Simplifying x + 0.9 = 1.187434209 Reorder the terms: 0.9 + x = 1.187434209 Solving 0.9 + x = 1.187434209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = 1.187434209 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 1.187434209 + -0.9 x = 1.187434209 + -0.9 Combine like terms: 1.187434209 + -0.9 = 0.287434209 x = 0.287434209 Simplifying x = 0.287434209Subproblem 2
x + 0.9 = -1.187434209 Simplifying x + 0.9 = -1.187434209 Reorder the terms: 0.9 + x = -1.187434209 Solving 0.9 + x = -1.187434209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = -1.187434209 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -1.187434209 + -0.9 x = -1.187434209 + -0.9 Combine like terms: -1.187434209 + -0.9 = -2.087434209 x = -2.087434209 Simplifying x = -2.087434209Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.287434209, -2.087434209}Solution
x = {0.287434209, -2.087434209}
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