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Simplifying 15x2 + 18x + -9 = 0 Reorder the terms: -9 + 18x + 15x2 = 0 Solving -9 + 18x + 15x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + 6x + 5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + 6x + 5x2)' equal to zero and attempt to solve: Simplifying -3 + 6x + 5x2 = 0 Solving -3 + 6x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + 1.2x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 1.2x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 1.2x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 1.2x + x2 = 0 + 0.6 1.2x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 1.2x + x2 = 0.6 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = 0.6 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 0.6 + 0.36 Combine like terms: 0.6 + 0.36 = 0.96 0.36 + 1.2x + x2 = 0.96 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 0.96 Calculate the square root of the right side: 0.979795897 Break this problem into two subproblems by setting (x + 0.6) equal to 0.979795897 and -0.979795897.Subproblem 1
x + 0.6 = 0.979795897 Simplifying x + 0.6 = 0.979795897 Reorder the terms: 0.6 + x = 0.979795897 Solving 0.6 + x = 0.979795897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 0.979795897 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 0.979795897 + -0.6 x = 0.979795897 + -0.6 Combine like terms: 0.979795897 + -0.6 = 0.379795897 x = 0.379795897 Simplifying x = 0.379795897Subproblem 2
x + 0.6 = -0.979795897 Simplifying x + 0.6 = -0.979795897 Reorder the terms: 0.6 + x = -0.979795897 Solving 0.6 + x = -0.979795897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -0.979795897 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -0.979795897 + -0.6 x = -0.979795897 + -0.6 Combine like terms: -0.979795897 + -0.6 = -1.579795897 x = -1.579795897 Simplifying x = -1.579795897Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.379795897, -1.579795897}Solution
x = {0.379795897, -1.579795897}
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