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Simplifying 3x2 + 42x + -24 = 0 Reorder the terms: -24 + 42x + 3x2 = 0 Solving -24 + 42x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-8 + 14x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-8 + 14x + x2)' equal to zero and attempt to solve: Simplifying -8 + 14x + x2 = 0 Solving -8 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 14x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 14x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 14x + x2 = 0 + 8 14x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 14x + x2 = 8 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 8 + 49 Reorder the terms: 49 + 14x + x2 = 8 + 49 Combine like terms: 8 + 49 = 57 49 + 14x + x2 = 57 Factor a perfect square on the left side: (x + 7)(x + 7) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (x + 7) equal to 7.549834435 and -7.549834435.Subproblem 1
x + 7 = 7.549834435 Simplifying x + 7 = 7.549834435 Reorder the terms: 7 + x = 7.549834435 Solving 7 + x = 7.549834435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 7.549834435 + -7 Combine like terms: 7 + -7 = 0 0 + x = 7.549834435 + -7 x = 7.549834435 + -7 Combine like terms: 7.549834435 + -7 = 0.549834435 x = 0.549834435 Simplifying x = 0.549834435Subproblem 2
x + 7 = -7.549834435 Simplifying x + 7 = -7.549834435 Reorder the terms: 7 + x = -7.549834435 Solving 7 + x = -7.549834435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -7.549834435 + -7 Combine like terms: 7 + -7 = 0 0 + x = -7.549834435 + -7 x = -7.549834435 + -7 Combine like terms: -7.549834435 + -7 = -14.549834435 x = -14.549834435 Simplifying x = -14.549834435Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.549834435, -14.549834435}Solution
x = {0.549834435, -14.549834435}
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