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Simplifying 4x2 + 88x + 336 = 0 Reorder the terms: 336 + 88x + 4x2 = 0 Solving 336 + 88x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(84 + 22x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(84 + 22x + x2)' equal to zero and attempt to solve: Simplifying 84 + 22x + x2 = 0 Solving 84 + 22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-84' to each side of the equation. 84 + 22x + -84 + x2 = 0 + -84 Reorder the terms: 84 + -84 + 22x + x2 = 0 + -84 Combine like terms: 84 + -84 = 0 0 + 22x + x2 = 0 + -84 22x + x2 = 0 + -84 Combine like terms: 0 + -84 = -84 22x + x2 = -84 The x term is 22x. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22x + 121 + x2 = -84 + 121 Reorder the terms: 121 + 22x + x2 = -84 + 121 Combine like terms: -84 + 121 = 37 121 + 22x + x2 = 37 Factor a perfect square on the left side: (x + 11)(x + 11) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (x + 11) equal to 6.08276253 and -6.08276253.Subproblem 1
x + 11 = 6.08276253 Simplifying x + 11 = 6.08276253 Reorder the terms: 11 + x = 6.08276253 Solving 11 + x = 6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 6.08276253 + -11 Combine like terms: 11 + -11 = 0 0 + x = 6.08276253 + -11 x = 6.08276253 + -11 Combine like terms: 6.08276253 + -11 = -4.91723747 x = -4.91723747 Simplifying x = -4.91723747Subproblem 2
x + 11 = -6.08276253 Simplifying x + 11 = -6.08276253 Reorder the terms: 11 + x = -6.08276253 Solving 11 + x = -6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -6.08276253 + -11 Combine like terms: 11 + -11 = 0 0 + x = -6.08276253 + -11 x = -6.08276253 + -11 Combine like terms: -6.08276253 + -11 = -17.08276253 x = -17.08276253 Simplifying x = -17.08276253Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.91723747, -17.08276253}Solution
x = {-4.91723747, -17.08276253}
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