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Simplifying 240 + 788x + 6x2 = 0 Solving 240 + 788x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(120 + 394x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(120 + 394x + 3x2)' equal to zero and attempt to solve: Simplifying 120 + 394x + 3x2 = 0 Solving 120 + 394x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 40 + 131.3333333x + x2 = 0 Move the constant term to the right: Add '-40' to each side of the equation. 40 + 131.3333333x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + 131.3333333x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + 131.3333333x + x2 = 0 + -40 131.3333333x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 131.3333333x + x2 = -40 The x term is 131.3333333x. Take half its coefficient (65.66666665). Square it (4312.111109) and add it to both sides. Add '4312.111109' to each side of the equation. 131.3333333x + 4312.111109 + x2 = -40 + 4312.111109 Reorder the terms: 4312.111109 + 131.3333333x + x2 = -40 + 4312.111109 Combine like terms: -40 + 4312.111109 = 4272.111109 4312.111109 + 131.3333333x + x2 = 4272.111109 Factor a perfect square on the left side: (x + 65.66666665)(x + 65.66666665) = 4272.111109 Calculate the square root of the right side: 65.361388518 Break this problem into two subproblems by setting (x + 65.66666665) equal to 65.361388518 and -65.361388518.Subproblem 1
x + 65.66666665 = 65.361388518 Simplifying x + 65.66666665 = 65.361388518 Reorder the terms: 65.66666665 + x = 65.361388518 Solving 65.66666665 + x = 65.361388518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-65.66666665' to each side of the equation. 65.66666665 + -65.66666665 + x = 65.361388518 + -65.66666665 Combine like terms: 65.66666665 + -65.66666665 = 0.00000000 0.00000000 + x = 65.361388518 + -65.66666665 x = 65.361388518 + -65.66666665 Combine like terms: 65.361388518 + -65.66666665 = -0.305278132 x = -0.305278132 Simplifying x = -0.305278132Subproblem 2
x + 65.66666665 = -65.361388518 Simplifying x + 65.66666665 = -65.361388518 Reorder the terms: 65.66666665 + x = -65.361388518 Solving 65.66666665 + x = -65.361388518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-65.66666665' to each side of the equation. 65.66666665 + -65.66666665 + x = -65.361388518 + -65.66666665 Combine like terms: 65.66666665 + -65.66666665 = 0.00000000 0.00000000 + x = -65.361388518 + -65.66666665 x = -65.361388518 + -65.66666665 Combine like terms: -65.361388518 + -65.66666665 = -131.028055168 x = -131.028055168 Simplifying x = -131.028055168Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.305278132, -131.028055168}Solution
x = {-0.305278132, -131.028055168}
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