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Simplifying -16x2 + 45x + 100 = 0 Reorder the terms: 100 + 45x + -16x2 = 0 Solving 100 + 45x + -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'. -6.25 + -2.8125x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -2.8125x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -2.8125x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -2.8125x + x2 = 0 + 6.25 -2.8125x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -2.8125x + x2 = 6.25 The x term is -2.8125x. Take half its coefficient (-1.40625). Square it (1.977539063) and add it to both sides. Add '1.977539063' to each side of the equation. -2.8125x + 1.977539063 + x2 = 6.25 + 1.977539063 Reorder the terms: 1.977539063 + -2.8125x + x2 = 6.25 + 1.977539063 Combine like terms: 6.25 + 1.977539063 = 8.227539063 1.977539063 + -2.8125x + x2 = 8.227539063 Factor a perfect square on the left side: (x + -1.40625)(x + -1.40625) = 8.227539063 Calculate the square root of the right side: 2.868368711 Break this problem into two subproblems by setting (x + -1.40625) equal to 2.868368711 and -2.868368711.Subproblem 1
x + -1.40625 = 2.868368711 Simplifying x + -1.40625 = 2.868368711 Reorder the terms: -1.40625 + x = 2.868368711 Solving -1.40625 + x = 2.868368711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + x = 2.868368711 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + x = 2.868368711 + 1.40625 x = 2.868368711 + 1.40625 Combine like terms: 2.868368711 + 1.40625 = 4.274618711 x = 4.274618711 Simplifying x = 4.274618711Subproblem 2
x + -1.40625 = -2.868368711 Simplifying x + -1.40625 = -2.868368711 Reorder the terms: -1.40625 + x = -2.868368711 Solving -1.40625 + x = -2.868368711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + x = -2.868368711 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + x = -2.868368711 + 1.40625 x = -2.868368711 + 1.40625 Combine like terms: -2.868368711 + 1.40625 = -1.462118711 x = -1.462118711 Simplifying x = -1.462118711Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.274618711, -1.462118711}
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