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Simplifying 16x2 + -136x + -33 = 0 Reorder the terms: -33 + -136x + 16x2 = 0 Solving -33 + -136x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -2.0625 + -8.5x + x2 = 0 Move the constant term to the right: Add '2.0625' to each side of the equation. -2.0625 + -8.5x + 2.0625 + x2 = 0 + 2.0625 Reorder the terms: -2.0625 + 2.0625 + -8.5x + x2 = 0 + 2.0625 Combine like terms: -2.0625 + 2.0625 = 0.0000 0.0000 + -8.5x + x2 = 0 + 2.0625 -8.5x + x2 = 0 + 2.0625 Combine like terms: 0 + 2.0625 = 2.0625 -8.5x + x2 = 2.0625 The x term is -8.5x. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5x + 18.0625 + x2 = 2.0625 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = 2.0625 + 18.0625 Combine like terms: 2.0625 + 18.0625 = 20.125 18.0625 + -8.5x + x2 = 20.125 Factor a perfect square on the left side: (x + -4.25)(x + -4.25) = 20.125 Calculate the square root of the right side: 4.486089611 Break this problem into two subproblems by setting (x + -4.25) equal to 4.486089611 and -4.486089611.Subproblem 1
x + -4.25 = 4.486089611 Simplifying x + -4.25 = 4.486089611 Reorder the terms: -4.25 + x = 4.486089611 Solving -4.25 + x = 4.486089611 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = 4.486089611 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 4.486089611 + 4.25 x = 4.486089611 + 4.25 Combine like terms: 4.486089611 + 4.25 = 8.736089611 x = 8.736089611 Simplifying x = 8.736089611Subproblem 2
x + -4.25 = -4.486089611 Simplifying x + -4.25 = -4.486089611 Reorder the terms: -4.25 + x = -4.486089611 Solving -4.25 + x = -4.486089611 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = -4.486089611 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -4.486089611 + 4.25 x = -4.486089611 + 4.25 Combine like terms: -4.486089611 + 4.25 = -0.236089611 x = -0.236089611 Simplifying x = -0.236089611Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.736089611, -0.236089611}
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