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Simplifying 0 = -16x2 + 160x + 4 Reorder the terms: 0 = 4 + 160x + -16x2 Solving 0 = 4 + 160x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + -160x + 16x2 = 4 + 160x + -16x2 + -4 + -160x + 16x2 Reorder the terms: -4 + -160x + 16x2 = 4 + -4 + 160x + -160x + -16x2 + 16x2 Combine like terms: 4 + -4 = 0 -4 + -160x + 16x2 = 0 + 160x + -160x + -16x2 + 16x2 -4 + -160x + 16x2 = 160x + -160x + -16x2 + 16x2 Combine like terms: 160x + -160x = 0 -4 + -160x + 16x2 = 0 + -16x2 + 16x2 -4 + -160x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -4 + -160x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + -40x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -40x + 4x2)' equal to zero and attempt to solve: Simplifying -1 + -40x + 4x2 = 0 Solving -1 + -40x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -10x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -10x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -10x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -10x + x2 = 0 + 0.25 -10x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -10x + x2 = 0.25 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 0.25 + 25 Reorder the terms: 25 + -10x + x2 = 0.25 + 25 Combine like terms: 0.25 + 25 = 25.25 25 + -10x + x2 = 25.25 Factor a perfect square on the left side: (x + -5)(x + -5) = 25.25 Calculate the square root of the right side: 5.024937811 Break this problem into two subproblems by setting (x + -5) equal to 5.024937811 and -5.024937811.Subproblem 1
x + -5 = 5.024937811 Simplifying x + -5 = 5.024937811 Reorder the terms: -5 + x = 5.024937811 Solving -5 + x = 5.024937811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 5.024937811 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.024937811 + 5 x = 5.024937811 + 5 Combine like terms: 5.024937811 + 5 = 10.024937811 x = 10.024937811 Simplifying x = 10.024937811Subproblem 2
x + -5 = -5.024937811 Simplifying x + -5 = -5.024937811 Reorder the terms: -5 + x = -5.024937811 Solving -5 + x = -5.024937811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -5.024937811 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.024937811 + 5 x = -5.024937811 + 5 Combine like terms: -5.024937811 + 5 = -0.024937811 x = -0.024937811 Simplifying x = -0.024937811Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.024937811, -0.024937811}Solution
x = {10.024937811, -0.024937811}
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