Respuesta :
Answer:
x=0.5355 or x=-6.5355
First step is to: Isolate the constant term by adding 7 to both sides
Step-by-step explanation:
We want to solve this equation: [tex]2x^2 + 12x - 7 = 0[/tex]
On observation, the trinomial is not factorizable so we use the Completing the square method.
Step 1: Isolate the constant term by adding 7 to both sides
[tex]2x^2 + 12x - 7+7 = 0+7\\2x^2 + 12x=7[/tex]
Step 2: Divide the equation all through by the coefficient of [tex]x^2[/tex] which is 2.
[tex]x^2 + 6x=\frac{7}{2}[/tex]
Step 3: Divide the coefficient of x by 2, square it and add it to both sides.
Coefficient of x=6
Divided by 2=3
Square of 3=[tex]3^2[/tex]
Therefore, we have:
[tex]x^2 + 6x+3^2=\frac{7}{2}+3^2[/tex]
Step 4: Write the Left Hand side in the form [tex](x+k)^2[/tex]
[tex](x+3)^2=\frac{7}{2}+3^2\\(x+3)^2=12.5\\[/tex]
Step 5: Take the square root of both sides and solve for x
[tex]x+3=\pm\sqrt{12.5}\\x=-3\pm \sqrt{12.5}\\x=-3+ \sqrt{12.5}, $ or $x= -3- \sqrt{12.5}\\$x=0.5355 or x=-6.5355[/tex]
Answer:
Step-by-step explanation:
Step 1: Isolate the constant term by adding 7 to both sides of the equation.
Step 2: Factor 2 from the binomial.
Step 3: 9
Step 3 b: 18
Step4: write the trinomial as the square root of a binomial.
Step 5: divide both sides of the equation by 2 Step
6: Apply the square root property of equality Step
7: subtract 3 from both sides of the equation.
