Question

solve each equation.

1. ( x^2 + 7x - 10 + 3 = x )

florida edgems math - algebra 1
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Explanation:

Step1: Simplify the equation

First, combine like terms on the left side. The equation is \(x^{2}+7x - 10 + 3=x\). Combine \(- 10\) and \(3\) to get \(x^{2}+7x-7 = x\).

Step2: Move all terms to one side

Subtract \(x\) from both sides to get a quadratic equation in standard form: \(x^{2}+7x - x-7 = 0\), which simplifies to \(x^{2}+6x - 7=0\).

Step3: Factor the quadratic equation

We need to find two numbers that multiply to \(-7\) and add up to \(6\). The numbers are \(7\) and \(- 1\). So, we can factor the equation as \((x + 7)(x-1)=0\).

Step4: Solve for \(x\)

Set each factor equal to zero and solve for \(x\):

• For \(x + 7=0\), we get \(x=-7\).
• For \(x - 1=0\), we get \(x = 1\).

Answer:

The solutions of the equation \(x^{2}+7x - 10 + 3=x\) are \(x=-7\) and \(x = 1\).