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Simplifying 16x2 + -20x + -45 = 0 Reorder the terms: -45 + -20x + 16x2 = 0 Solving -45 + -20x + 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'. -2.8125 + -1.25x + x2 = 0 Move the constant term to the right: Add '2.8125' to each side of the equation. -2.8125 + -1.25x + 2.8125 + x2 = 0 + 2.8125 Reorder the terms: -2.8125 + 2.8125 + -1.25x + x2 = 0 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + -1.25x + x2 = 0 + 2.8125 -1.25x + x2 = 0 + 2.8125 Combine like terms: 0 + 2.8125 = 2.8125 -1.25x + x2 = 2.8125 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 2.8125 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 2.8125 + 0.390625 Combine like terms: 2.8125 + 0.390625 = 3.203125 0.390625 + -1.25x + x2 = 3.203125 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 3.203125 Calculate the square root of the right side: 1.789727633 Break this problem into two subproblems by setting (x + -0.625) equal to 1.789727633 and -1.789727633.Subproblem 1
x + -0.625 = 1.789727633 Simplifying x + -0.625 = 1.789727633 Reorder the terms: -0.625 + x = 1.789727633 Solving -0.625 + x = 1.789727633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 1.789727633 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 1.789727633 + 0.625 x = 1.789727633 + 0.625 Combine like terms: 1.789727633 + 0.625 = 2.414727633 x = 2.414727633 Simplifying x = 2.414727633Subproblem 2
x + -0.625 = -1.789727633 Simplifying x + -0.625 = -1.789727633 Reorder the terms: -0.625 + x = -1.789727633 Solving -0.625 + x = -1.789727633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -1.789727633 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -1.789727633 + 0.625 x = -1.789727633 + 0.625 Combine like terms: -1.789727633 + 0.625 = -1.164727633 x = -1.164727633 Simplifying x = -1.164727633Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.414727633, -1.164727633}
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