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Simplifying 2x2 + 3x + 1 = 100 Reorder the terms: 1 + 3x + 2x2 = 100 Solving 1 + 3x + 2x2 = 100 Solving for variable 'x'. Reorder the terms: 1 + -100 + 3x + 2x2 = 100 + -100 Combine like terms: 1 + -100 = -99 -99 + 3x + 2x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -99 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -49.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '49.5' to each side of the equation. -49.5 + 1.5x + 49.5 + x2 = 0 + 49.5 Reorder the terms: -49.5 + 49.5 + 1.5x + x2 = 0 + 49.5 Combine like terms: -49.5 + 49.5 = 0.0 0.0 + 1.5x + x2 = 0 + 49.5 1.5x + x2 = 0 + 49.5 Combine like terms: 0 + 49.5 = 49.5 1.5x + x2 = 49.5 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 49.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 49.5 + 0.5625 Combine like terms: 49.5 + 0.5625 = 50.0625 0.5625 + 1.5x + x2 = 50.0625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 50.0625 Calculate the square root of the right side: 7.075485849 Break this problem into two subproblems by setting (x + 0.75) equal to 7.075485849 and -7.075485849.Subproblem 1
x + 0.75 = 7.075485849 Simplifying x + 0.75 = 7.075485849 Reorder the terms: 0.75 + x = 7.075485849 Solving 0.75 + x = 7.075485849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 7.075485849 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 7.075485849 + -0.75 x = 7.075485849 + -0.75 Combine like terms: 7.075485849 + -0.75 = 6.325485849 x = 6.325485849 Simplifying x = 6.325485849Subproblem 2
x + 0.75 = -7.075485849 Simplifying x + 0.75 = -7.075485849 Reorder the terms: 0.75 + x = -7.075485849 Solving 0.75 + x = -7.075485849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -7.075485849 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -7.075485849 + -0.75 x = -7.075485849 + -0.75 Combine like terms: -7.075485849 + -0.75 = -7.825485849 x = -7.825485849 Simplifying x = -7.825485849Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.325485849, -7.825485849}
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