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Simplifying 4x2 + 16x + -52 = 0 Reorder the terms: -52 + 16x + 4x2 = 0 Solving -52 + 16x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-13 + 4x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-13 + 4x + x2)' equal to zero and attempt to solve: Simplifying -13 + 4x + x2 = 0 Solving -13 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 4x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 4x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 4x + x2 = 0 + 13 4x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 4x + x2 = 13 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 13 + 4 Reorder the terms: 4 + 4x + x2 = 13 + 4 Combine like terms: 13 + 4 = 17 4 + 4x + x2 = 17 Factor a perfect square on the left side: (x + 2)(x + 2) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x + 2) equal to 4.123105626 and -4.123105626.Subproblem 1
x + 2 = 4.123105626 Simplifying x + 2 = 4.123105626 Reorder the terms: 2 + x = 4.123105626 Solving 2 + x = 4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 4.123105626 + -2 Combine like terms: 2 + -2 = 0 0 + x = 4.123105626 + -2 x = 4.123105626 + -2 Combine like terms: 4.123105626 + -2 = 2.123105626 x = 2.123105626 Simplifying x = 2.123105626Subproblem 2
x + 2 = -4.123105626 Simplifying x + 2 = -4.123105626 Reorder the terms: 2 + x = -4.123105626 Solving 2 + x = -4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -4.123105626 + -2 Combine like terms: 2 + -2 = 0 0 + x = -4.123105626 + -2 x = -4.123105626 + -2 Combine like terms: -4.123105626 + -2 = -6.123105626 x = -6.123105626 Simplifying x = -6.123105626Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.123105626, -6.123105626}Solution
x = {2.123105626, -6.123105626}
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