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Simplifying 15x2 + 9x + -27 = 0 Reorder the terms: -27 + 9x + 15x2 = 0 Solving -27 + 9x + 15x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-9 + 3x + 5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-9 + 3x + 5x2)' equal to zero and attempt to solve: Simplifying -9 + 3x + 5x2 = 0 Solving -9 + 3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.8 + 0.6x + x2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 0.6x + 1.8 + x2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + 0.6x + x2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 0.6x + x2 = 0 + 1.8 0.6x + x2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 0.6x + x2 = 1.8 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 1.8 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 1.8 + 0.09 Combine like terms: 1.8 + 0.09 = 1.89 0.09 + 0.6x + x2 = 1.89 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 1.89 Calculate the square root of the right side: 1.374772708 Break this problem into two subproblems by setting (x + 0.3) equal to 1.374772708 and -1.374772708.Subproblem 1
x + 0.3 = 1.374772708 Simplifying x + 0.3 = 1.374772708 Reorder the terms: 0.3 + x = 1.374772708 Solving 0.3 + x = 1.374772708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 1.374772708 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 1.374772708 + -0.3 x = 1.374772708 + -0.3 Combine like terms: 1.374772708 + -0.3 = 1.074772708 x = 1.074772708 Simplifying x = 1.074772708Subproblem 2
x + 0.3 = -1.374772708 Simplifying x + 0.3 = -1.374772708 Reorder the terms: 0.3 + x = -1.374772708 Solving 0.3 + x = -1.374772708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -1.374772708 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -1.374772708 + -0.3 x = -1.374772708 + -0.3 Combine like terms: -1.374772708 + -0.3 = -1.674772708 x = -1.674772708 Simplifying x = -1.674772708Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.074772708, -1.674772708}Solution
x = {1.074772708, -1.674772708}
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