How to solve this quadratic equation by factoring?
10x2 - 19x -15 = 0
To solve a quadratic equation by factoring, follow these steps:
Step 1: Write the quadratic equation in the standard form, ax^2 + bx + c = 0. In this case, the quadratic equation is 10x^2 - 19x - 15 = 0.
Step 2: Factor the quadratic equation. Look for two numbers that multiply to give the product of a * c (the coefficient of x^2 multiplied by the constant term), and add up to give b (the coefficient of x). In this case, the product of 10 * -15 is -150, and we need two numbers that add up to -19.
Step 3: Rewrite the quadratic equation using the factored form. Using the numbers we found in step 2, rewrite the equation. For example, if the two numbers that add up to -19 are -20 and 1, then the factored form of the quadratic equation would be (10x + 1)(x - 15) = 0.
Step 4: Set each factor equal to zero and solve for x. Now, using the factored form from step 3, set each factor equal to zero:
10x + 1 = 0 and x - 15 = 0
Solving these two equations will give us the values of x.
For 10x + 1 = 0, subtract 1 from both sides and divide by 10:
10x = -1
x = -1/10
For x - 15 = 0, add 15 to both sides:
x = 15
Step 5: Check the solutions. Substitute the values of x into the original equation and make sure they satisfy the equation. In this case, when you substitute x = -1/10 or x = 15 into the original equation (10x^2 - 19x - 15 = 0), both values will satisfy the equation.
Therefore, the solutions to the quadratic equation 10x^2 - 19x - 15 = 0 are x = -1/10 and x = 15, obtained by factoring the equation.