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Simplifying 2x2 + 7x = 9801 Reorder the terms: 7x + 2x2 = 9801 Solving 7x + 2x2 = 9801 Solving for variable 'x'. Reorder the terms: -9801 + 7x + 2x2 = 9801 + -9801 Combine like terms: 9801 + -9801 = 0 -9801 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4900.5 + 3.5x + x2 = 0 Move the constant term to the right: Add '4900.5' to each side of the equation. -4900.5 + 3.5x + 4900.5 + x2 = 0 + 4900.5 Reorder the terms: -4900.5 + 4900.5 + 3.5x + x2 = 0 + 4900.5 Combine like terms: -4900.5 + 4900.5 = 0.0 0.0 + 3.5x + x2 = 0 + 4900.5 3.5x + x2 = 0 + 4900.5 Combine like terms: 0 + 4900.5 = 4900.5 3.5x + x2 = 4900.5 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 4900.5 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 4900.5 + 3.0625 Combine like terms: 4900.5 + 3.0625 = 4903.5625 3.0625 + 3.5x + x2 = 4903.5625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 4903.5625 Calculate the square root of the right side: 70.025441805 Break this problem into two subproblems by setting (x + 1.75) equal to 70.025441805 and -70.025441805.Subproblem 1
x + 1.75 = 70.025441805 Simplifying x + 1.75 = 70.025441805 Reorder the terms: 1.75 + x = 70.025441805 Solving 1.75 + x = 70.025441805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 70.025441805 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 70.025441805 + -1.75 x = 70.025441805 + -1.75 Combine like terms: 70.025441805 + -1.75 = 68.275441805 x = 68.275441805 Simplifying x = 68.275441805Subproblem 2
x + 1.75 = -70.025441805 Simplifying x + 1.75 = -70.025441805 Reorder the terms: 1.75 + x = -70.025441805 Solving 1.75 + x = -70.025441805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -70.025441805 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -70.025441805 + -1.75 x = -70.025441805 + -1.75 Combine like terms: -70.025441805 + -1.75 = -71.775441805 x = -71.775441805 Simplifying x = -71.775441805Solution
The solution to the problem is based on the solutions from the subproblems. x = {68.275441805, -71.775441805}
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