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Simplifying 0 = 4x2 + 40x + -120 Reorder the terms: 0 = -120 + 40x + 4x2 Solving 0 = -120 + 40x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 120 = 120 120 + -40x + -4x2 = -120 + 40x + 4x2 + 120 + -40x + -4x2 Reorder the terms: 120 + -40x + -4x2 = -120 + 120 + 40x + -40x + 4x2 + -4x2 Combine like terms: -120 + 120 = 0 120 + -40x + -4x2 = 0 + 40x + -40x + 4x2 + -4x2 120 + -40x + -4x2 = 40x + -40x + 4x2 + -4x2 Combine like terms: 40x + -40x = 0 120 + -40x + -4x2 = 0 + 4x2 + -4x2 120 + -40x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 120 + -40x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(30 + -10x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(30 + -10x + -1x2)' equal to zero and attempt to solve: Simplifying 30 + -10x + -1x2 = 0 Solving 30 + -10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -30 + 10x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 10x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 10x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 10x + x2 = 0 + 30 10x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 10x + x2 = 30 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 = 30 + 25 Reorder the terms: 25 + 10x + x2 = 30 + 25 Combine like terms: 30 + 25 = 55 25 + 10x + x2 = 55 Factor a perfect square on the left side: (x + 5)(x + 5) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (x + 5) equal to 7.416198487 and -7.416198487.Subproblem 1
x + 5 = 7.416198487 Simplifying x + 5 = 7.416198487 Reorder the terms: 5 + x = 7.416198487 Solving 5 + x = 7.416198487 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 = 7.416198487 + -5 Combine like terms: 5 + -5 = 0 0 + x = 7.416198487 + -5 x = 7.416198487 + -5 Combine like terms: 7.416198487 + -5 = 2.416198487 x = 2.416198487 Simplifying x = 2.416198487Subproblem 2
x + 5 = -7.416198487 Simplifying x + 5 = -7.416198487 Reorder the terms: 5 + x = -7.416198487 Solving 5 + x = -7.416198487 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 = -7.416198487 + -5 Combine like terms: 5 + -5 = 0 0 + x = -7.416198487 + -5 x = -7.416198487 + -5 Combine like terms: -7.416198487 + -5 = -12.416198487 x = -12.416198487 Simplifying x = -12.416198487Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.416198487, -12.416198487}Solution
x = {2.416198487, -12.416198487}
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