quadratic equation

If x2 is added to x, the sum is 42. x^2 + x = 42 Subtract 42 from both sides: x^2 + x - 42 = 0 We have a quadratic equation. Using our quadratic equation solver, we get: x = 6 and x = -7 Since the problem does not state positive number solutions, they are both answers.

The sum of the squares of two consecutive positive integers is 61. Find these two numbers. Let the 2 consecutive integers be x and x + 1. We have: x^2 + (x + 1)^2 = 61 Simplify: x^2 + x^2 + 2x + 1 = 61 2x^2 + 2x + 1 = 61 Subtract 61 from each side: 2x^2 + 2x - 60 = 0 Divide each side by 2...

2x^2+4x < 3x+6 Subtract 3x from both sides: 2x^2 + x < 6 Subtract 6 from both sides 2x^2 + x - 6 < 0 Using our quadratic calculator, we get: x < 1.5 and x < -2 When we take the intersection of these, it's x < 1.5

The sum of a number and its square is 72. find the numbers? Let the number be n. We have: n^2 + n = 72 Subtract 72 from each side: n^2 + n - 72 = 0 Using our quadratic calculator, we have: n = 8 or n = -9 Since the numbers do not state positive or negative, these are the two solutions.

Let x be the number. We have: x^2 + x = 30 Subtract 30 from each side: x^2 + x - 30 = 0 Using our quadratic calculator, we get potential solutions of: x = 5 or x = -6 Check 5: 5 + 5^2 = 5 + 25 = 30 Check -6 -6 + -6^2 = -6 + 36 = 30