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Simplifying -3x2 + -27x + 42 = 0 Reorder the terms: 42 + -27x + -3x2 = 0 Solving 42 + -27x + -3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(14 + -9x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(14 + -9x + -1x2)' equal to zero and attempt to solve: Simplifying 14 + -9x + -1x2 = 0 Solving 14 + -9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -14 + 9x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 9x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + 9x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 9x + x2 = 0 + 14 9x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 9x + x2 = 14 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 14 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 14 + 20.25 Combine like terms: 14 + 20.25 = 34.25 20.25 + 9x + x2 = 34.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 34.25 Calculate the square root of the right side: 5.852349955 Break this problem into two subproblems by setting (x + 4.5) equal to 5.852349955 and -5.852349955.Subproblem 1
x + 4.5 = 5.852349955 Simplifying x + 4.5 = 5.852349955 Reorder the terms: 4.5 + x = 5.852349955 Solving 4.5 + x = 5.852349955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 5.852349955 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 5.852349955 + -4.5 x = 5.852349955 + -4.5 Combine like terms: 5.852349955 + -4.5 = 1.352349955 x = 1.352349955 Simplifying x = 1.352349955Subproblem 2
x + 4.5 = -5.852349955 Simplifying x + 4.5 = -5.852349955 Reorder the terms: 4.5 + x = -5.852349955 Solving 4.5 + x = -5.852349955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -5.852349955 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -5.852349955 + -4.5 x = -5.852349955 + -4.5 Combine like terms: -5.852349955 + -4.5 = -10.352349955 x = -10.352349955 Simplifying x = -10.352349955Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.352349955, -10.352349955}Solution
x = {1.352349955, -10.352349955}
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