Question

Me ajude a resolver essa equação
x²-3x+4=-7x+10

Answer 1

Explicação passo-a-passo:

x²-3x+4=-7x+10

x²-3x + 7x + 4 - 10= 0

x² + 4x - 6 = 0

a= 1; b = 4; c = -6

Δ = b² - 4ac

Δ = 4² - 4 . 1 . (-6)

Δ = 16 + 24

Δ = 40

x = (-b ± √Δ)/2a

x = ( - 4 ± √40)/2 . 1

x = ( - 4 ± √40)/2

x = ( - 4 ± 2√10)/2

x = - 2 ± √10

x' = - 2 + √10

x" = - 2 - √10

Answer 2

$\red{x_{1} = - 2 \sqrt{10} \: \: \: \: \: \: x_{2} = - 2 + \sqrt{10} }$

Explicação passo a passo:

$\orange{x {}^{2} - 3x + 4 = - 7x + 10 } \\ x {}^{2} - 3x + 4 = - 7x + 10 \\ x {}^{2} - 3x +4 + 7x - 10 = - 7x + 10 + 7x - 10 \\x {}^{2} - 3x + 4 + 7x - 10 = 0 \\ x {}^{2} - 3x + 4 = - 7x + 10 \\x {}^{2} - 3x + 4 + 7x - 10 = 0 \\ - 3x + 7x \\ ( - 3 + 7)x \\ 4x \\ x {}^{2} - 3x + 4 + 7x - 10 = 0 \\ x {}^{2} + 4x + 4 - 10 = 0\\x {}^{2} - 3x + 4 + 7x -10 = 0 \\4 - 10\\ - (10 - 4) \\ - 6 \\x {}^{2} - 3x + 4 + 7x - 10 = 0\\x {}^{2} + 4x - 6 = 0 \\1x {}^{2} + 4x - 6 = 0 \\ 1x{}^{2} + 4x + ( - 6) = 0 \\ a = 1 \: \: \: \: \: \: b = 4 \: \: \: \: \: c = - 6 \\ x {}^{2} + 4x - 6 = 0 \\ a = 1 \: \: \: \: b = 4 \: \: \: \: c - 6 \\ x = \frac{ - 4 + \sqrt{4 {}^{2} - 4 \times1 \times ( - 6) } }{2 \times 1} \\ \\ x = \frac{ - 4 + \sqrt{4 {}^{2} - 4 \div ( - 6) } }{2 \times 1} \\ \\ x = \frac{ - 4 + \sqrt{4 {}^{2} - 4 \times ( - 6) }}{2} \\ \\ x = \frac{ - 4 + \sqrt{4 {}^{2} - 4 \times 1 \times ( - 6) } }{2 \times 1} \\ \\ 4 {}^{2} \\ 4 \times 4 \\ 16 \\ x = \frac{ - 4 + \sqrt{4 {}^{2} - 4 \times 1 \times ( - 6) } }{2 \times 1} \\ \\ x = \frac{ - 4 + \sqrt{16 - 4 \times( - 6) } }{2} \\ \\</strong></p><p>[tex]x = \frac{ - 4 + \sqrt{4 {}^{2} - 4 \times 1 \times ( - 6)} }{2 \times 1} \\ \\ - 4 \times ( - 6) \\ 4 \times 6 \\ 24 \\ x = \frac{ - 4 + \sqrt{4 {}^{2} - 4 \times 1 \times ( - 6) } }{2 \times 1} \\ \\ x = \frac{ - 4 + \sqrt{16 + 24} }{2} \\ \\ x = \frac{ - 4 + \sqrt{40} }{2} \\ \\ \sqrt{40} \\ \sqrt{4 \times 10} \\ \sqrt{2 {}^{2} \times 10} \\ \sqrt{2 {}^{2} } \sqrt{10} \\ 2 \sqrt{10} \\ x = \frac{ - 4 + \sqrt{10} }{2} \\ \\ x = \frac{ - 4 + 2 \sqrt{10} }{2} \\ \\ x = \frac{ - 4 + \sqrt{10} }{2} \\ \\ x = \frac{ - 4 - 2 \sqrt{10} }{2} \\ \\ \frac{ - 4 + 2 \sqrt{10} }{2} \\ \\ \frac{ - 4 + 2 \sqrt{10} }{2} \\ \\ \frac{2( - 2 + \sqrt{10)} }{2} \\ \\ - 2 + \sqrt{10} \\ x = \frac{ - 4 + 2 \sqrt{10} }{2} \\ \\ x = \frac{ - 4 - 2 \sqrt{10} }{2} \\ \\ x = - 2 + \sqrt{10} \\ x = \frac{ - 4 - 2 \sqrt{10} }{2} \\ \\ \frac{ - 4 - 2 \sqrt{10} }{2} \\ \\ \frac{2( - 2 - \sqrt{10}) }{2} \\ - 2 - \sqrt{10} \\ x = \frac{ - 4 + 2 \sqrt{10} }{2} \\ \\ x = \frac{ - 4 - 2 \sqrt{10} }{2} \\ \\ x = - 2 + \sqrt{10} \\ x = - 2 - \sqrt{10} \\ x_{1} = - 2 - \sqrt{10} \: \: \: \: \: x_{2} - 2 + \sqrt{10} \\ resposta \\ \pink{x_{1} = - 2 - \sqrt{10} \: \: \: \: \: \: \: x_{2} = - 2 + \sqrt{10} }$