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Simplifying 2x2 + 8x + -912 = 0 Reorder the terms: -912 + 8x + 2x2 = 0 Solving -912 + 8x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-456 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-456 + 4x + x2)' equal to zero and attempt to solve: Simplifying -456 + 4x + x2 = 0 Solving -456 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '456' to each side of the equation. -456 + 4x + 456 + x2 = 0 + 456 Reorder the terms: -456 + 456 + 4x + x2 = 0 + 456 Combine like terms: -456 + 456 = 0 0 + 4x + x2 = 0 + 456 4x + x2 = 0 + 456 Combine like terms: 0 + 456 = 456 4x + x2 = 456 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 = 456 + 4 Reorder the terms: 4 + 4x + x2 = 456 + 4 Combine like terms: 456 + 4 = 460 4 + 4x + x2 = 460 Factor a perfect square on the left side: (x + 2)(x + 2) = 460 Calculate the square root of the right side: 21.44761059 Break this problem into two subproblems by setting (x + 2) equal to 21.44761059 and -21.44761059.Subproblem 1
x + 2 = 21.44761059 Simplifying x + 2 = 21.44761059 Reorder the terms: 2 + x = 21.44761059 Solving 2 + x = 21.44761059 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 = 21.44761059 + -2 Combine like terms: 2 + -2 = 0 0 + x = 21.44761059 + -2 x = 21.44761059 + -2 Combine like terms: 21.44761059 + -2 = 19.44761059 x = 19.44761059 Simplifying x = 19.44761059Subproblem 2
x + 2 = -21.44761059 Simplifying x + 2 = -21.44761059 Reorder the terms: 2 + x = -21.44761059 Solving 2 + x = -21.44761059 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 = -21.44761059 + -2 Combine like terms: 2 + -2 = 0 0 + x = -21.44761059 + -2 x = -21.44761059 + -2 Combine like terms: -21.44761059 + -2 = -23.44761059 x = -23.44761059 Simplifying x = -23.44761059Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.44761059, -23.44761059}Solution
x = {19.44761059, -23.44761059}
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