Solve the quadratic by factoring.
x, squared, minus, 14, x, plus, 4, equals, minus, 10, x, plus, 9
x
2
−14x+4=−10x+9
To solve the quadratic equation x^2 - 14x + 4 = -10x + 9, the first step is to move all terms to one side to obtain a quadratic equation in standard form:
x^2 - 14x + 10x + 4 - 9 = 0
Simplifying:
x^2 - 4x - 5 = 0
Next, we need to factor the quadratic equation.
The factored form is:
(x - 5)(x + 1) = 0
Setting each factor equal to zero:
x - 5 = 0 or x + 1 = 0
Solving for x:
x = 5 or x = -1
Therefore, the solutions to the quadratic equation x^2 - 14x + 4 = -10x + 9 are x = 5 and x = -1.
To solve the quadratic equation by factoring, you need to set the equation equal to zero first.
x^2 - 14x + 4 = -10x + 9
Now, move all terms to one side of the equation to get:
x^2 - 14x + 10x + 4 - 9 = 0
Combine like terms:
x^2 - 4x - 5 = 0
Next, factor the quadratic equation. For this equation, you'll need to find two numbers that multiply to -5 and add up to -4. The numbers -5 and 1 fit this criterion.
(x - 5)(x + 1) = 0
Now, set each factor equal to zero and solve for x:
x - 5 = 0 or x + 1 = 0
For the first equation, add 5 to both sides:
x = 5
For the second equation, subtract 1 from both sides:
x = -1
Therefore, the solution to the quadratic equation is x = 5 or x = -1.
To solve the quadratic equation by factoring, we need to rearrange the equation into the form of Ax^2 + Bx + C = 0. Let's start by doing that:
x^2 - 14x + 4 = -10x + 9
Now, let's bring all the terms to one side of the equation to set it equal to zero:
x^2 - 14x + 10x + 4 - 9 = 0
Simplifying further:
x^2 - 4x - 5 = 0
Now, we need to factor this quadratic equation. Let's find two numbers that when multiplied give us -5 and when added give us -4. Those numbers are -5 and +1.
(x - 5)(x + 1) = 0
According to the zero-product property, if the product of two factors is equal to zero, then at least one of the factors must be zero. So, we have two possibilities:
x - 5 = 0 or x + 1 = 0
Solving each equation:
If x - 5 = 0, then x = 5
If x + 1 = 0, then x = -1
Therefore, the solutions to the quadratic equation are x = 5 and x = -1.