```Question 189892

Notice we have a quadratic equation in the form of {{{ah^2+bh+c}}} where {{{a=-2}}}, {{{b=-28}}}, and {{{c=-98}}}

Let's use the quadratic formula to solve for h

{{{h = (-(-28) +- sqrt( (-28)^2-4(-2)(-98) ))/(2(-2))}}} Plug in  {{{a=-2}}}, {{{b=-28}}}, and {{{c=-98}}}

{{{h = (28 +- sqrt( (-28)^2-4(-2)(-98) ))/(2(-2))}}} Negate {{{-28}}} to get {{{28}}}.

{{{h = (28 +- sqrt( 784-4(-2)(-98) ))/(2(-2))}}} Square {{{-28}}} to get {{{784}}}.

{{{h = (28 +- sqrt( 784-784 ))/(2(-2))}}} Multiply {{{4(-2)(-98)}}} to get {{{784}}}

{{{h = (28 +- sqrt( 0 ))/(2(-2))}}} Subtract {{{784}}} from {{{784}}} to get {{{0}}}

{{{h = (28 +- sqrt( 0 ))/(-4)}}} Multiply {{{2}}} and {{{-2}}} to get {{{-4}}}.

{{{h = (28 +- 0)/(-4)}}} Take the square root of {{{0}}} to get {{{0}}}.

{{{h = (28 + 0)/(-4)}}} or {{{h = (28 - 0)/(-4)}}} Break up the expression.

{{{h = (28)/(-4)}}} or {{{h =  (28)/(-4)}}} Combine like terms.

{{{h = -7}}} or {{{h = -7}}} Simplify.

So the answer is {{{h = -7}}}

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