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Simplifying 2x2 + 24x + -224 = 0 Reorder the terms: -224 + 24x + 2x2 = 0 Solving -224 + 24x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-112 + 12x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-112 + 12x + x2)' equal to zero and attempt to solve: Simplifying -112 + 12x + x2 = 0 Solving -112 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '112' to each side of the equation. -112 + 12x + 112 + x2 = 0 + 112 Reorder the terms: -112 + 112 + 12x + x2 = 0 + 112 Combine like terms: -112 + 112 = 0 0 + 12x + x2 = 0 + 112 12x + x2 = 0 + 112 Combine like terms: 0 + 112 = 112 12x + x2 = 112 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 112 + 36 Reorder the terms: 36 + 12x + x2 = 112 + 36 Combine like terms: 112 + 36 = 148 36 + 12x + x2 = 148 Factor a perfect square on the left side: (x + 6)(x + 6) = 148 Calculate the square root of the right side: 12.165525061 Break this problem into two subproblems by setting (x + 6) equal to 12.165525061 and -12.165525061.Subproblem 1
x + 6 = 12.165525061 Simplifying x + 6 = 12.165525061 Reorder the terms: 6 + x = 12.165525061 Solving 6 + x = 12.165525061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 12.165525061 + -6 Combine like terms: 6 + -6 = 0 0 + x = 12.165525061 + -6 x = 12.165525061 + -6 Combine like terms: 12.165525061 + -6 = 6.165525061 x = 6.165525061 Simplifying x = 6.165525061Subproblem 2
x + 6 = -12.165525061 Simplifying x + 6 = -12.165525061 Reorder the terms: 6 + x = -12.165525061 Solving 6 + x = -12.165525061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -12.165525061 + -6 Combine like terms: 6 + -6 = 0 0 + x = -12.165525061 + -6 x = -12.165525061 + -6 Combine like terms: -12.165525061 + -6 = -18.165525061 x = -18.165525061 Simplifying x = -18.165525061Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.165525061, -18.165525061}Solution
x = {6.165525061, -18.165525061}
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