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Simplifying 0 = -16x2 + 21x + 210 Reorder the terms: 0 = 210 + 21x + -16x2 Solving 0 = 210 + 21x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -210 = -210 -210 + -21x + 16x2 = 210 + 21x + -16x2 + -210 + -21x + 16x2 Reorder the terms: -210 + -21x + 16x2 = 210 + -210 + 21x + -21x + -16x2 + 16x2 Combine like terms: 210 + -210 = 0 -210 + -21x + 16x2 = 0 + 21x + -21x + -16x2 + 16x2 -210 + -21x + 16x2 = 21x + -21x + -16x2 + 16x2 Combine like terms: 21x + -21x = 0 -210 + -21x + 16x2 = 0 + -16x2 + 16x2 -210 + -21x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -210 + -21x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -13.125 + -1.3125x + x2 = 0 Move the constant term to the right: Add '13.125' to each side of the equation. -13.125 + -1.3125x + 13.125 + x2 = 0 + 13.125 Reorder the terms: -13.125 + 13.125 + -1.3125x + x2 = 0 + 13.125 Combine like terms: -13.125 + 13.125 = 0.000 0.000 + -1.3125x + x2 = 0 + 13.125 -1.3125x + x2 = 0 + 13.125 Combine like terms: 0 + 13.125 = 13.125 -1.3125x + x2 = 13.125 The x term is -1.3125x. Take half its coefficient (-0.65625). Square it (0.4306640625) and add it to both sides. Add '0.4306640625' to each side of the equation. -1.3125x + 0.4306640625 + x2 = 13.125 + 0.4306640625 Reorder the terms: 0.4306640625 + -1.3125x + x2 = 13.125 + 0.4306640625 Combine like terms: 13.125 + 0.4306640625 = 13.5556640625 0.4306640625 + -1.3125x + x2 = 13.5556640625 Factor a perfect square on the left side: (x + -0.65625)(x + -0.65625) = 13.5556640625 Calculate the square root of the right side: 3.681801741 Break this problem into two subproblems by setting (x + -0.65625) equal to 3.681801741 and -3.681801741.Subproblem 1
x + -0.65625 = 3.681801741 Simplifying x + -0.65625 = 3.681801741 Reorder the terms: -0.65625 + x = 3.681801741 Solving -0.65625 + x = 3.681801741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.65625' to each side of the equation. -0.65625 + 0.65625 + x = 3.681801741 + 0.65625 Combine like terms: -0.65625 + 0.65625 = 0.00000 0.00000 + x = 3.681801741 + 0.65625 x = 3.681801741 + 0.65625 Combine like terms: 3.681801741 + 0.65625 = 4.338051741 x = 4.338051741 Simplifying x = 4.338051741Subproblem 2
x + -0.65625 = -3.681801741 Simplifying x + -0.65625 = -3.681801741 Reorder the terms: -0.65625 + x = -3.681801741 Solving -0.65625 + x = -3.681801741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.65625' to each side of the equation. -0.65625 + 0.65625 + x = -3.681801741 + 0.65625 Combine like terms: -0.65625 + 0.65625 = 0.00000 0.00000 + x = -3.681801741 + 0.65625 x = -3.681801741 + 0.65625 Combine like terms: -3.681801741 + 0.65625 = -3.025551741 x = -3.025551741 Simplifying x = -3.025551741Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.338051741, -3.025551741}
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