Pergunta

Solve for all values of x by factoring. x^2-4x-32=0 Answer Attempt 1 out of 3 x=square
Solução

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MárcioVeterano · Tutor por 10 anos
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To solve the quadratic equation \(x^2 - 4x - 32 = 0\) by factoring, we need to find two numbers that multiply to \(-32\) and add up to \(-4\).<br /><br />The quadratic equation is in the form \(ax^2 + bx + c = 0\), where \(a = 1\), \(b = -4\), and \(c = -32\).<br /><br />We need to find two numbers whose product is \(ac = 1 \cdot (-32) = -32\) and whose sum is \(b = -4\).<br /><br />The numbers that satisfy these conditions are \(-8\) and \(4\), because:<br />\[<br />-8 \cdot 4 = -32 \quad \text{and} \quad -8 + 4 = -4<br />\]<br /><br />So, we can factor the quadratic equation as:<br />\[<br />(x - 8)(x + 4) = 0<br />\]<br /><br />Setting each factor equal to zero gives us the solutions:<br />\[<br />x - 8 = 0 \quad \text{or} \quad x + 4 = 0<br />\]<br /><br />Solving these equations, we get:<br />\[<br />x = 8 \quad \text{or} \quad x = -4<br />\]<br /><br />Therefore, the solutions to the equation \(x^2 - 4x - 32 = 0\) are:<br />\[<br />x = 8 \quad \text{and} \quad x = -4<br />\]
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