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Simplifying 3x2 + 30x + -24 = 0 Reorder the terms: -24 + 30x + 3x2 = 0 Solving -24 + 30x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-8 + 10x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-8 + 10x + x2)' equal to zero and attempt to solve: Simplifying -8 + 10x + x2 = 0 Solving -8 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 10x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 10x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 10x + x2 = 0 + 8 10x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 10x + x2 = 8 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 8 + 25 Reorder the terms: 25 + 10x + x2 = 8 + 25 Combine like terms: 8 + 25 = 33 25 + 10x + x2 = 33 Factor a perfect square on the left side: (x + 5)(x + 5) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (x + 5) equal to 5.744562647 and -5.744562647.Subproblem 1
x + 5 = 5.744562647 Simplifying x + 5 = 5.744562647 Reorder the terms: 5 + x = 5.744562647 Solving 5 + x = 5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 5.744562647 + -5 Combine like terms: 5 + -5 = 0 0 + x = 5.744562647 + -5 x = 5.744562647 + -5 Combine like terms: 5.744562647 + -5 = 0.744562647 x = 0.744562647 Simplifying x = 0.744562647Subproblem 2
x + 5 = -5.744562647 Simplifying x + 5 = -5.744562647 Reorder the terms: 5 + x = -5.744562647 Solving 5 + x = -5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -5.744562647 + -5 Combine like terms: 5 + -5 = 0 0 + x = -5.744562647 + -5 x = -5.744562647 + -5 Combine like terms: -5.744562647 + -5 = -10.744562647 x = -10.744562647 Simplifying x = -10.744562647Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.744562647, -10.744562647}Solution
x = {0.744562647, -10.744562647}
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