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# Help. ​

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Help.

NotSoSmart  Nov 2, 2017

#1
+5258
+1

1.     -4x2 - 3x + 2  =  0       Here,  a = -4 ,  b = -3 ,  and  c = 2  .

$$x = {-b \pm \sqrt{b^2-4ac} \over 2a} \\~\\ x = {-(-3) \pm \sqrt{(-3)^2-4(-4)(2)} \over 2(-4)} \\~\\ x = {3 \pm \sqrt{9+32} \over -8} \\~\\ x = {3 \pm \sqrt{41} \over -8} \\~\\ x = -\frac{3}{8}\pm\frac{\sqrt{41}}{8}$$

2.     h2 + 5h  =  295     This is the equation we need to solve. Subtract  295  from both sides.

h2 + 5h - 295  =  0       Now this is a quadratic equation with  x = h,  a = 1 ,  b = 5 ,  and  c = -295  .

$$x = {-b \pm \sqrt{b^2-4ac} \over 2a} \\~\\ h = {-5 \pm \sqrt{5^2-4(1)(-295)} \over 2(1)} \\~\\ h = {-5 \pm \sqrt{25+1180} \over 2} \\~\\ h = {-5 + \sqrt{1205} \over 2}\qquad\text{or}\qquad h = {-5 - \sqrt{1205} \over 2}$$

At this point, lets just plug both of these into a calculator to get

h  ≈  14.86   or   h  ≈  -19.86

h  is a distance, so the answer is  14.86 yards .

hectictar  Nov 2, 2017
Sort:

#1
+5258
+1

1.     -4x2 - 3x + 2  =  0       Here,  a = -4 ,  b = -3 ,  and  c = 2  .

$$x = {-b \pm \sqrt{b^2-4ac} \over 2a} \\~\\ x = {-(-3) \pm \sqrt{(-3)^2-4(-4)(2)} \over 2(-4)} \\~\\ x = {3 \pm \sqrt{9+32} \over -8} \\~\\ x = {3 \pm \sqrt{41} \over -8} \\~\\ x = -\frac{3}{8}\pm\frac{\sqrt{41}}{8}$$

2.     h2 + 5h  =  295     This is the equation we need to solve. Subtract  295  from both sides.

h2 + 5h - 295  =  0       Now this is a quadratic equation with  x = h,  a = 1 ,  b = 5 ,  and  c = -295  .

$$x = {-b \pm \sqrt{b^2-4ac} \over 2a} \\~\\ h = {-5 \pm \sqrt{5^2-4(1)(-295)} \over 2(1)} \\~\\ h = {-5 \pm \sqrt{25+1180} \over 2} \\~\\ h = {-5 + \sqrt{1205} \over 2}\qquad\text{or}\qquad h = {-5 - \sqrt{1205} \over 2}$$

At this point, lets just plug both of these into a calculator to get

h  ≈  14.86   or   h  ≈  -19.86

h  is a distance, so the answer is  14.86 yards .

hectictar  Nov 2, 2017

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