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Simplifying -9x[5x2 + -3x + -6] = 0 Reorder the terms: -9x[-6 + -3x + 5x2] = 0 [-6 * -9x + -3x * -9x + 5x2 * -9x] = 0 [54x + 27x2 + -45x3] = 0 Solving 54x + 27x2 + -45x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9x'. 9x(6 + 3x + -5x2) = 0 Ignore the factor 9.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(6 + 3x + -5x2)' equal to zero and attempt to solve: Simplifying 6 + 3x + -5x2 = 0 Solving 6 + 3x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.2 + -0.6x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -0.6x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -0.6x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -0.6x + x2 = 0 + 1.2 -0.6x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -0.6x + x2 = 1.2 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 = 1.2 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 1.2 + 0.09 Combine like terms: 1.2 + 0.09 = 1.29 0.09 + -0.6x + x2 = 1.29 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 1.29 Calculate the square root of the right side: 1.135781669 Break this problem into two subproblems by setting (x + -0.3) equal to 1.135781669 and -1.135781669.Subproblem 1
x + -0.3 = 1.135781669 Simplifying x + -0.3 = 1.135781669 Reorder the terms: -0.3 + x = 1.135781669 Solving -0.3 + x = 1.135781669 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 = 1.135781669 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 1.135781669 + 0.3 x = 1.135781669 + 0.3 Combine like terms: 1.135781669 + 0.3 = 1.435781669 x = 1.435781669 Simplifying x = 1.435781669Subproblem 2
x + -0.3 = -1.135781669 Simplifying x + -0.3 = -1.135781669 Reorder the terms: -0.3 + x = -1.135781669 Solving -0.3 + x = -1.135781669 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 = -1.135781669 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -1.135781669 + 0.3 x = -1.135781669 + 0.3 Combine like terms: -1.135781669 + 0.3 = -0.835781669 x = -0.835781669 Simplifying x = -0.835781669Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.435781669, -0.835781669}Solution
x = {0, 1.435781669, -0.835781669}
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