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Simplifying 3x2 + 42x = -117 Reorder the terms: 42x + 3x2 = -117 Solving 42x + 3x2 = -117 Solving for variable 'x'. Reorder the terms: 117 + 42x + 3x2 = -117 + 117 Combine like terms: -117 + 117 = 0 117 + 42x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(39 + 14x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(39 + 14x + x2)' equal to zero and attempt to solve: Simplifying 39 + 14x + x2 = 0 Solving 39 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-39' to each side of the equation. 39 + 14x + -39 + x2 = 0 + -39 Reorder the terms: 39 + -39 + 14x + x2 = 0 + -39 Combine like terms: 39 + -39 = 0 0 + 14x + x2 = 0 + -39 14x + x2 = 0 + -39 Combine like terms: 0 + -39 = -39 14x + x2 = -39 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 = -39 + 49 Reorder the terms: 49 + 14x + x2 = -39 + 49 Combine like terms: -39 + 49 = 10 49 + 14x + x2 = 10 Factor a perfect square on the left side: (x + 7)(x + 7) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + 7) equal to 3.16227766 and -3.16227766.Subproblem 1
x + 7 = 3.16227766 Simplifying x + 7 = 3.16227766 Reorder the terms: 7 + x = 3.16227766 Solving 7 + x = 3.16227766 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 = 3.16227766 + -7 Combine like terms: 7 + -7 = 0 0 + x = 3.16227766 + -7 x = 3.16227766 + -7 Combine like terms: 3.16227766 + -7 = -3.83772234 x = -3.83772234 Simplifying x = -3.83772234Subproblem 2
x + 7 = -3.16227766 Simplifying x + 7 = -3.16227766 Reorder the terms: 7 + x = -3.16227766 Solving 7 + x = -3.16227766 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 = -3.16227766 + -7 Combine like terms: 7 + -7 = 0 0 + x = -3.16227766 + -7 x = -3.16227766 + -7 Combine like terms: -3.16227766 + -7 = -10.16227766 x = -10.16227766 Simplifying x = -10.16227766Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.83772234, -10.16227766}Solution
x = {-3.83772234, -10.16227766}
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