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Simplifying 2x(x + -4) = 222 Reorder the terms: 2x(-4 + x) = 222 (-4 * 2x + x * 2x) = 222 (-8x + 2x2) = 222 Solving -8x + 2x2 = 222 Solving for variable 'x'. Reorder the terms: -222 + -8x + 2x2 = 222 + -222 Combine like terms: 222 + -222 = 0 -222 + -8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-111 + -4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-111 + -4x + x2)' equal to zero and attempt to solve: Simplifying -111 + -4x + x2 = 0 Solving -111 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '111' to each side of the equation. -111 + -4x + 111 + x2 = 0 + 111 Reorder the terms: -111 + 111 + -4x + x2 = 0 + 111 Combine like terms: -111 + 111 = 0 0 + -4x + x2 = 0 + 111 -4x + x2 = 0 + 111 Combine like terms: 0 + 111 = 111 -4x + x2 = 111 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 = 111 + 4 Reorder the terms: 4 + -4x + x2 = 111 + 4 Combine like terms: 111 + 4 = 115 4 + -4x + x2 = 115 Factor a perfect square on the left side: (x + -2)(x + -2) = 115 Calculate the square root of the right side: 10.723805295 Break this problem into two subproblems by setting (x + -2) equal to 10.723805295 and -10.723805295.Subproblem 1
x + -2 = 10.723805295 Simplifying x + -2 = 10.723805295 Reorder the terms: -2 + x = 10.723805295 Solving -2 + x = 10.723805295 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 = 10.723805295 + 2 Combine like terms: -2 + 2 = 0 0 + x = 10.723805295 + 2 x = 10.723805295 + 2 Combine like terms: 10.723805295 + 2 = 12.723805295 x = 12.723805295 Simplifying x = 12.723805295Subproblem 2
x + -2 = -10.723805295 Simplifying x + -2 = -10.723805295 Reorder the terms: -2 + x = -10.723805295 Solving -2 + x = -10.723805295 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 = -10.723805295 + 2 Combine like terms: -2 + 2 = 0 0 + x = -10.723805295 + 2 x = -10.723805295 + 2 Combine like terms: -10.723805295 + 2 = -8.723805295 x = -8.723805295 Simplifying x = -8.723805295Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.723805295, -8.723805295}Solution
x = {12.723805295, -8.723805295}
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