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Simplifying -16x + -4(x(x)) = -420 Multiply x * x -16x + -4(x2) = -420 Solving -16x + -4x2 = -420 Solving for variable 'x'. Reorder the terms: 420 + -16x + -4x2 = -420 + 420 Combine like terms: -420 + 420 = 0 420 + -16x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(105 + -4x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(105 + -4x + -1x2)' equal to zero and attempt to solve: Simplifying 105 + -4x + -1x2 = 0 Solving 105 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -105 + 4x + x2 = 0 Move the constant term to the right: Add '105' to each side of the equation. -105 + 4x + 105 + x2 = 0 + 105 Reorder the terms: -105 + 105 + 4x + x2 = 0 + 105 Combine like terms: -105 + 105 = 0 0 + 4x + x2 = 0 + 105 4x + x2 = 0 + 105 Combine like terms: 0 + 105 = 105 4x + x2 = 105 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 = 105 + 4 Reorder the terms: 4 + 4x + x2 = 105 + 4 Combine like terms: 105 + 4 = 109 4 + 4x + x2 = 109 Factor a perfect square on the left side: (x + 2)(x + 2) = 109 Calculate the square root of the right side: 10.440306509 Break this problem into two subproblems by setting (x + 2) equal to 10.440306509 and -10.440306509.Subproblem 1
x + 2 = 10.440306509 Simplifying x + 2 = 10.440306509 Reorder the terms: 2 + x = 10.440306509 Solving 2 + x = 10.440306509 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 = 10.440306509 + -2 Combine like terms: 2 + -2 = 0 0 + x = 10.440306509 + -2 x = 10.440306509 + -2 Combine like terms: 10.440306509 + -2 = 8.440306509 x = 8.440306509 Simplifying x = 8.440306509Subproblem 2
x + 2 = -10.440306509 Simplifying x + 2 = -10.440306509 Reorder the terms: 2 + x = -10.440306509 Solving 2 + x = -10.440306509 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 = -10.440306509 + -2 Combine like terms: 2 + -2 = 0 0 + x = -10.440306509 + -2 x = -10.440306509 + -2 Combine like terms: -10.440306509 + -2 = -12.440306509 x = -12.440306509 Simplifying x = -12.440306509Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.440306509, -12.440306509}Solution
x = {8.440306509, -12.440306509}
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