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Simplifying 2x2 + -9x = 100 Reorder the terms: -9x + 2x2 = 100 Solving -9x + 2x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + -9x + 2x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -50 + -4.5x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + -4.5x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + -4.5x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -4.5x + x2 = 0 + 50 -4.5x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 -4.5x + x2 = 50 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 50 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 50 + 5.0625 Combine like terms: 50 + 5.0625 = 55.0625 5.0625 + -4.5x + x2 = 55.0625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 55.0625 Calculate the square root of the right side: 7.42041104 Break this problem into two subproblems by setting (x + -2.25) equal to 7.42041104 and -7.42041104.Subproblem 1
x + -2.25 = 7.42041104 Simplifying x + -2.25 = 7.42041104 Reorder the terms: -2.25 + x = 7.42041104 Solving -2.25 + x = 7.42041104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 7.42041104 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 7.42041104 + 2.25 x = 7.42041104 + 2.25 Combine like terms: 7.42041104 + 2.25 = 9.67041104 x = 9.67041104 Simplifying x = 9.67041104Subproblem 2
x + -2.25 = -7.42041104 Simplifying x + -2.25 = -7.42041104 Reorder the terms: -2.25 + x = -7.42041104 Solving -2.25 + x = -7.42041104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -7.42041104 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -7.42041104 + 2.25 x = -7.42041104 + 2.25 Combine like terms: -7.42041104 + 2.25 = -5.17041104 x = -5.17041104 Simplifying x = -5.17041104Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.67041104, -5.17041104}
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