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Simplifying 0 = 5 + 15x + -16x2 Solving 0 = 5 + 15x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -5 = -5 -5 + -15x + 16x2 = 5 + 15x + -16x2 + -5 + -15x + 16x2 Reorder the terms: -5 + -15x + 16x2 = 5 + -5 + 15x + -15x + -16x2 + 16x2 Combine like terms: 5 + -5 = 0 -5 + -15x + 16x2 = 0 + 15x + -15x + -16x2 + 16x2 -5 + -15x + 16x2 = 15x + -15x + -16x2 + 16x2 Combine like terms: 15x + -15x = 0 -5 + -15x + 16x2 = 0 + -16x2 + 16x2 -5 + -15x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -5 + -15x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.3125 + -0.9375x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -0.9375x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -0.9375x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -0.9375x + x2 = 0 + 0.3125 -0.9375x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -0.9375x + x2 = 0.3125 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 = 0.3125 + 0.2197265625 Reorder the terms: 0.2197265625 + -0.9375x + x2 = 0.3125 + 0.2197265625 Combine like terms: 0.3125 + 0.2197265625 = 0.5322265625 0.2197265625 + -0.9375x + x2 = 0.5322265625 Factor a perfect square on the left side: (x + -0.46875)(x + -0.46875) = 0.5322265625 Calculate the square root of the right side: 0.729538596 Break this problem into two subproblems by setting (x + -0.46875) equal to 0.729538596 and -0.729538596.Subproblem 1
x + -0.46875 = 0.729538596 Simplifying x + -0.46875 = 0.729538596 Reorder the terms: -0.46875 + x = 0.729538596 Solving -0.46875 + x = 0.729538596 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 = 0.729538596 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + x = 0.729538596 + 0.46875 x = 0.729538596 + 0.46875 Combine like terms: 0.729538596 + 0.46875 = 1.198288596 x = 1.198288596 Simplifying x = 1.198288596Subproblem 2
x + -0.46875 = -0.729538596 Simplifying x + -0.46875 = -0.729538596 Reorder the terms: -0.46875 + x = -0.729538596 Solving -0.46875 + x = -0.729538596 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 = -0.729538596 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + x = -0.729538596 + 0.46875 x = -0.729538596 + 0.46875 Combine like terms: -0.729538596 + 0.46875 = -0.260788596 x = -0.260788596 Simplifying x = -0.260788596Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.198288596, -0.260788596}
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