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Simplifying 3x2 + 6x + -351 = 0 Reorder the terms: -351 + 6x + 3x2 = 0 Solving -351 + 6x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-117 + 2x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-117 + 2x + x2)' equal to zero and attempt to solve: Simplifying -117 + 2x + x2 = 0 Solving -117 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '117' to each side of the equation. -117 + 2x + 117 + x2 = 0 + 117 Reorder the terms: -117 + 117 + 2x + x2 = 0 + 117 Combine like terms: -117 + 117 = 0 0 + 2x + x2 = 0 + 117 2x + x2 = 0 + 117 Combine like terms: 0 + 117 = 117 2x + x2 = 117 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 117 + 1 Reorder the terms: 1 + 2x + x2 = 117 + 1 Combine like terms: 117 + 1 = 118 1 + 2x + x2 = 118 Factor a perfect square on the left side: (x + 1)(x + 1) = 118 Calculate the square root of the right side: 10.862780491 Break this problem into two subproblems by setting (x + 1) equal to 10.862780491 and -10.862780491.Subproblem 1
x + 1 = 10.862780491 Simplifying x + 1 = 10.862780491 Reorder the terms: 1 + x = 10.862780491 Solving 1 + x = 10.862780491 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 10.862780491 + -1 Combine like terms: 1 + -1 = 0 0 + x = 10.862780491 + -1 x = 10.862780491 + -1 Combine like terms: 10.862780491 + -1 = 9.862780491 x = 9.862780491 Simplifying x = 9.862780491Subproblem 2
x + 1 = -10.862780491 Simplifying x + 1 = -10.862780491 Reorder the terms: 1 + x = -10.862780491 Solving 1 + x = -10.862780491 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -10.862780491 + -1 Combine like terms: 1 + -1 = 0 0 + x = -10.862780491 + -1 x = -10.862780491 + -1 Combine like terms: -10.862780491 + -1 = -11.862780491 x = -11.862780491 Simplifying x = -11.862780491Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.862780491, -11.862780491}Solution
x = {9.862780491, -11.862780491}
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