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Simplifying 2x2 + -4x = 420 Reorder the terms: -4x + 2x2 = 420 Solving -4x + 2x2 = 420 Solving for variable 'x'. Reorder the terms: -420 + -4x + 2x2 = 420 + -420 Combine like terms: 420 + -420 = 0 -420 + -4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-210 + -2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-210 + -2x + x2)' equal to zero and attempt to solve: Simplifying -210 + -2x + x2 = 0 Solving -210 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '210' to each side of the equation. -210 + -2x + 210 + x2 = 0 + 210 Reorder the terms: -210 + 210 + -2x + x2 = 0 + 210 Combine like terms: -210 + 210 = 0 0 + -2x + x2 = 0 + 210 -2x + x2 = 0 + 210 Combine like terms: 0 + 210 = 210 -2x + x2 = 210 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 210 + 1 Reorder the terms: 1 + -2x + x2 = 210 + 1 Combine like terms: 210 + 1 = 211 1 + -2x + x2 = 211 Factor a perfect square on the left side: (x + -1)(x + -1) = 211 Calculate the square root of the right side: 14.525839046 Break this problem into two subproblems by setting (x + -1) equal to 14.525839046 and -14.525839046.Subproblem 1
x + -1 = 14.525839046 Simplifying x + -1 = 14.525839046 Reorder the terms: -1 + x = 14.525839046 Solving -1 + x = 14.525839046 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 14.525839046 + 1 Combine like terms: -1 + 1 = 0 0 + x = 14.525839046 + 1 x = 14.525839046 + 1 Combine like terms: 14.525839046 + 1 = 15.525839046 x = 15.525839046 Simplifying x = 15.525839046Subproblem 2
x + -1 = -14.525839046 Simplifying x + -1 = -14.525839046 Reorder the terms: -1 + x = -14.525839046 Solving -1 + x = -14.525839046 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -14.525839046 + 1 Combine like terms: -1 + 1 = 0 0 + x = -14.525839046 + 1 x = -14.525839046 + 1 Combine like terms: -14.525839046 + 1 = -13.525839046 x = -13.525839046 Simplifying x = -13.525839046Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.525839046, -13.525839046}Solution
x = {15.525839046, -13.525839046}
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