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Simplifying 4x2 + 42x + -220 = 0 Reorder the terms: -220 + 42x + 4x2 = 0 Solving -220 + 42x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-110 + 21x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-110 + 21x + 2x2)' equal to zero and attempt to solve: Simplifying -110 + 21x + 2x2 = 0 Solving -110 + 21x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -55 + 10.5x + x2 = 0 Move the constant term to the right: Add '55' to each side of the equation. -55 + 10.5x + 55 + x2 = 0 + 55 Reorder the terms: -55 + 55 + 10.5x + x2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + 10.5x + x2 = 0 + 55 10.5x + x2 = 0 + 55 Combine like terms: 0 + 55 = 55 10.5x + x2 = 55 The x term is 10.5x. Take half its coefficient (5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. 10.5x + 27.5625 + x2 = 55 + 27.5625 Reorder the terms: 27.5625 + 10.5x + x2 = 55 + 27.5625 Combine like terms: 55 + 27.5625 = 82.5625 27.5625 + 10.5x + x2 = 82.5625 Factor a perfect square on the left side: (x + 5.25)(x + 5.25) = 82.5625 Calculate the square root of the right side: 9.086390923 Break this problem into two subproblems by setting (x + 5.25) equal to 9.086390923 and -9.086390923.Subproblem 1
x + 5.25 = 9.086390923 Simplifying x + 5.25 = 9.086390923 Reorder the terms: 5.25 + x = 9.086390923 Solving 5.25 + x = 9.086390923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = 9.086390923 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 9.086390923 + -5.25 x = 9.086390923 + -5.25 Combine like terms: 9.086390923 + -5.25 = 3.836390923 x = 3.836390923 Simplifying x = 3.836390923Subproblem 2
x + 5.25 = -9.086390923 Simplifying x + 5.25 = -9.086390923 Reorder the terms: 5.25 + x = -9.086390923 Solving 5.25 + x = -9.086390923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = -9.086390923 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -9.086390923 + -5.25 x = -9.086390923 + -5.25 Combine like terms: -9.086390923 + -5.25 = -14.336390923 x = -14.336390923 Simplifying x = -14.336390923Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.836390923, -14.336390923}Solution
x = {3.836390923, -14.336390923}
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