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Simplifying -16x2 + 112x + 20 = 0 Reorder the terms: 20 + 112x + -16x2 = 0 Solving 20 + 112x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(5 + 28x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + 28x + -4x2)' equal to zero and attempt to solve: Simplifying 5 + 28x + -4x2 = 0 Solving 5 + 28x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.25 + -7x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -7x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -7x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -7x + x2 = 0 + 1.25 -7x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -7x + x2 = 1.25 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 1.25 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 1.25 + 12.25 Combine like terms: 1.25 + 12.25 = 13.5 12.25 + -7x + x2 = 13.5 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 13.5 Calculate the square root of the right side: 3.674234614 Break this problem into two subproblems by setting (x + -3.5) equal to 3.674234614 and -3.674234614.Subproblem 1
x + -3.5 = 3.674234614 Simplifying x + -3.5 = 3.674234614 Reorder the terms: -3.5 + x = 3.674234614 Solving -3.5 + x = 3.674234614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.674234614 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.674234614 + 3.5 x = 3.674234614 + 3.5 Combine like terms: 3.674234614 + 3.5 = 7.174234614 x = 7.174234614 Simplifying x = 7.174234614Subproblem 2
x + -3.5 = -3.674234614 Simplifying x + -3.5 = -3.674234614 Reorder the terms: -3.5 + x = -3.674234614 Solving -3.5 + x = -3.674234614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.674234614 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.674234614 + 3.5 x = -3.674234614 + 3.5 Combine like terms: -3.674234614 + 3.5 = -0.174234614 x = -0.174234614 Simplifying x = -0.174234614Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.174234614, -0.174234614}Solution
x = {7.174234614, -0.174234614}
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