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Simplifying -16x2 + 5x + 950 = 0 Reorder the terms: 950 + 5x + -16x2 = 0 Solving 950 + 5x + -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'. -59.375 + -0.3125x + x2 = 0 Move the constant term to the right: Add '59.375' to each side of the equation. -59.375 + -0.3125x + 59.375 + x2 = 0 + 59.375 Reorder the terms: -59.375 + 59.375 + -0.3125x + x2 = 0 + 59.375 Combine like terms: -59.375 + 59.375 = 0.000 0.000 + -0.3125x + x2 = 0 + 59.375 -0.3125x + x2 = 0 + 59.375 Combine like terms: 0 + 59.375 = 59.375 -0.3125x + x2 = 59.375 The x term is -0.3125x. Take half its coefficient (-0.15625). Square it (0.0244140625) and add it to both sides. Add '0.0244140625' to each side of the equation. -0.3125x + 0.0244140625 + x2 = 59.375 + 0.0244140625 Reorder the terms: 0.0244140625 + -0.3125x + x2 = 59.375 + 0.0244140625 Combine like terms: 59.375 + 0.0244140625 = 59.3994140625 0.0244140625 + -0.3125x + x2 = 59.3994140625 Factor a perfect square on the left side: (x + -0.15625)(x + -0.15625) = 59.3994140625 Calculate the square root of the right side: 7.707101534 Break this problem into two subproblems by setting (x + -0.15625) equal to 7.707101534 and -7.707101534.Subproblem 1
x + -0.15625 = 7.707101534 Simplifying x + -0.15625 = 7.707101534 Reorder the terms: -0.15625 + x = 7.707101534 Solving -0.15625 + x = 7.707101534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + x = 7.707101534 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + x = 7.707101534 + 0.15625 x = 7.707101534 + 0.15625 Combine like terms: 7.707101534 + 0.15625 = 7.863351534 x = 7.863351534 Simplifying x = 7.863351534Subproblem 2
x + -0.15625 = -7.707101534 Simplifying x + -0.15625 = -7.707101534 Reorder the terms: -0.15625 + x = -7.707101534 Solving -0.15625 + x = -7.707101534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + x = -7.707101534 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + x = -7.707101534 + 0.15625 x = -7.707101534 + 0.15625 Combine like terms: -7.707101534 + 0.15625 = -7.550851534 x = -7.550851534 Simplifying x = -7.550851534Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.863351534, -7.550851534}
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