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Simplifying 1 = -16x2 + 20x + 300 Reorder the terms: 1 = 300 + 20x + -16x2 Solving 1 = 300 + 20x + -16x2 Solving for variable 'x'. Combine like terms: 1 + -300 = -299 -299 + -20x + 16x2 = 300 + 20x + -16x2 + -300 + -20x + 16x2 Reorder the terms: -299 + -20x + 16x2 = 300 + -300 + 20x + -20x + -16x2 + 16x2 Combine like terms: 300 + -300 = 0 -299 + -20x + 16x2 = 0 + 20x + -20x + -16x2 + 16x2 -299 + -20x + 16x2 = 20x + -20x + -16x2 + 16x2 Combine like terms: 20x + -20x = 0 -299 + -20x + 16x2 = 0 + -16x2 + 16x2 -299 + -20x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -299 + -20x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -18.6875 + -1.25x + x2 = 0 Move the constant term to the right: Add '18.6875' to each side of the equation. -18.6875 + -1.25x + 18.6875 + x2 = 0 + 18.6875 Reorder the terms: -18.6875 + 18.6875 + -1.25x + x2 = 0 + 18.6875 Combine like terms: -18.6875 + 18.6875 = 0.0000 0.0000 + -1.25x + x2 = 0 + 18.6875 -1.25x + x2 = 0 + 18.6875 Combine like terms: 0 + 18.6875 = 18.6875 -1.25x + x2 = 18.6875 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 = 18.6875 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 18.6875 + 0.390625 Combine like terms: 18.6875 + 0.390625 = 19.078125 0.390625 + -1.25x + x2 = 19.078125 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 19.078125 Calculate the square root of the right side: 4.367851302 Break this problem into two subproblems by setting (x + -0.625) equal to 4.367851302 and -4.367851302.Subproblem 1
x + -0.625 = 4.367851302 Simplifying x + -0.625 = 4.367851302 Reorder the terms: -0.625 + x = 4.367851302 Solving -0.625 + x = 4.367851302 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 = 4.367851302 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 4.367851302 + 0.625 x = 4.367851302 + 0.625 Combine like terms: 4.367851302 + 0.625 = 4.992851302 x = 4.992851302 Simplifying x = 4.992851302Subproblem 2
x + -0.625 = -4.367851302 Simplifying x + -0.625 = -4.367851302 Reorder the terms: -0.625 + x = -4.367851302 Solving -0.625 + x = -4.367851302 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 = -4.367851302 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -4.367851302 + 0.625 x = -4.367851302 + 0.625 Combine like terms: -4.367851302 + 0.625 = -3.742851302 x = -3.742851302 Simplifying x = -3.742851302Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.992851302, -3.742851302}
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