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Simplifying -16x2 + 48x + 160 = 20 Reorder the terms: 160 + 48x + -16x2 = 20 Solving 160 + 48x + -16x2 = 20 Solving for variable 'x'. Reorder the terms: 160 + -20 + 48x + -16x2 = 20 + -20 Combine like terms: 160 + -20 = 140 140 + 48x + -16x2 = 20 + -20 Combine like terms: 20 + -20 = 0 140 + 48x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(35 + 12x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(35 + 12x + -4x2)' equal to zero and attempt to solve: Simplifying 35 + 12x + -4x2 = 0 Solving 35 + 12x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -8.75 + -3x + x2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + -3x + 8.75 + x2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + -3x + x2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + -3x + x2 = 0 + 8.75 -3x + x2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 -3x + x2 = 8.75 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 8.75 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 8.75 + 2.25 Combine like terms: 8.75 + 2.25 = 11 2.25 + -3x + x2 = 11 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + -1.5) equal to 3.31662479 and -3.31662479.Subproblem 1
x + -1.5 = 3.31662479 Simplifying x + -1.5 = 3.31662479 Reorder the terms: -1.5 + x = 3.31662479 Solving -1.5 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 3.31662479 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.31662479 + 1.5 x = 3.31662479 + 1.5 Combine like terms: 3.31662479 + 1.5 = 4.81662479 x = 4.81662479 Simplifying x = 4.81662479Subproblem 2
x + -1.5 = -3.31662479 Simplifying x + -1.5 = -3.31662479 Reorder the terms: -1.5 + x = -3.31662479 Solving -1.5 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -3.31662479 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.31662479 + 1.5 x = -3.31662479 + 1.5 Combine like terms: -3.31662479 + 1.5 = -1.81662479 x = -1.81662479 Simplifying x = -1.81662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.81662479, -1.81662479}Solution
x = {4.81662479, -1.81662479}
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