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Simplifying 16x2 + -15x + -21 = 0 Reorder the terms: -21 + -15x + 16x2 = 0 Solving -21 + -15x + 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'. -1.3125 + -0.9375x + x2 = 0 Move the constant term to the right: Add '1.3125' to each side of the equation. -1.3125 + -0.9375x + 1.3125 + x2 = 0 + 1.3125 Reorder the terms: -1.3125 + 1.3125 + -0.9375x + x2 = 0 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + -0.9375x + x2 = 0 + 1.3125 -0.9375x + x2 = 0 + 1.3125 Combine like terms: 0 + 1.3125 = 1.3125 -0.9375x + x2 = 1.3125 The x term is -0.9375x. Take half its coefficient (-0.46875). Square it (0.2197265625) and add it to both sides. Add '0.2197265625' to each side of the equation. -0.9375x + 0.2197265625 + x2 = 1.3125 + 0.2197265625 Reorder the terms: 0.2197265625 + -0.9375x + x2 = 1.3125 + 0.2197265625 Combine like terms: 1.3125 + 0.2197265625 = 1.5322265625 0.2197265625 + -0.9375x + x2 = 1.5322265625 Factor a perfect square on the left side: (x + -0.46875)(x + -0.46875) = 1.5322265625 Calculate the square root of the right side: 1.237831395 Break this problem into two subproblems by setting (x + -0.46875) equal to 1.237831395 and -1.237831395.Subproblem 1
x + -0.46875 = 1.237831395 Simplifying x + -0.46875 = 1.237831395 Reorder the terms: -0.46875 + x = 1.237831395 Solving -0.46875 + x = 1.237831395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.46875' to each side of the equation. -0.46875 + 0.46875 + x = 1.237831395 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + x = 1.237831395 + 0.46875 x = 1.237831395 + 0.46875 Combine like terms: 1.237831395 + 0.46875 = 1.706581395 x = 1.706581395 Simplifying x = 1.706581395Subproblem 2
x + -0.46875 = -1.237831395 Simplifying x + -0.46875 = -1.237831395 Reorder the terms: -0.46875 + x = -1.237831395 Solving -0.46875 + x = -1.237831395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.46875' to each side of the equation. -0.46875 + 0.46875 + x = -1.237831395 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + x = -1.237831395 + 0.46875 x = -1.237831395 + 0.46875 Combine like terms: -1.237831395 + 0.46875 = -0.769081395 x = -0.769081395 Simplifying x = -0.769081395Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.706581395, -0.769081395}
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