9.7=-0.01x^2+0.26x+8.65

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Solution for 9.7=-0.01x^2+0.26x+8.65 equation:


Simplifying
9.7 = -0.01x2 + 0.26x + 8.65

Reorder the terms:
9.7 = 8.65 + 0.26x + -0.01x2

Solving
9.7 = 8.65 + 0.26x + -0.01x2

Solving for variable 'x'.

Combine like terms: 9.7 + -8.65 = 1.05
1.05 + -0.26x + 0.01x2 = 8.65 + 0.26x + -0.01x2 + -8.65 + -0.26x + 0.01x2

Reorder the terms:
1.05 + -0.26x + 0.01x2 = 8.65 + -8.65 + 0.26x + -0.26x + -0.01x2 + 0.01x2

Combine like terms: 8.65 + -8.65 = 0.00
1.05 + -0.26x + 0.01x2 = 0.00 + 0.26x + -0.26x + -0.01x2 + 0.01x2
1.05 + -0.26x + 0.01x2 = 0.26x + -0.26x + -0.01x2 + 0.01x2

Combine like terms: 0.26x + -0.26x = 0.00
1.05 + -0.26x + 0.01x2 = 0.00 + -0.01x2 + 0.01x2
1.05 + -0.26x + 0.01x2 = -0.01x2 + 0.01x2

Combine like terms: -0.01x2 + 0.01x2 = 0.00
1.05 + -0.26x + 0.01x2 = 0.00

Begin completing the square.  Divide all terms by
0.01 the coefficient of the squared term: 

Divide each side by '0.01'.
105 + -26x + x2 = 0

Move the constant term to the right:

Add '-105' to each side of the equation.
105 + -26x + -105 + x2 = 0 + -105

Reorder the terms:
105 + -105 + -26x + x2 = 0 + -105

Combine like terms: 105 + -105 = 0
0 + -26x + x2 = 0 + -105
-26x + x2 = 0 + -105

Combine like terms: 0 + -105 = -105
-26x + x2 = -105

The x term is -26x.  Take half its coefficient (-13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
-26x + 169 + x2 = -105 + 169

Reorder the terms:
169 + -26x + x2 = -105 + 169

Combine like terms: -105 + 169 = 64
169 + -26x + x2 = 64

Factor a perfect square on the left side:
(x + -13)(x + -13) = 64

Calculate the square root of the right side: 8

Break this problem into two subproblems by setting 
(x + -13) equal to 8 and -8.

Subproblem 1

x + -13 = 8 Simplifying x + -13 = 8 Reorder the terms: -13 + x = 8 Solving -13 + x = 8 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 8 + 13 Combine like terms: -13 + 13 = 0 0 + x = 8 + 13 x = 8 + 13 Combine like terms: 8 + 13 = 21 x = 21 Simplifying x = 21

Subproblem 2

x + -13 = -8 Simplifying x + -13 = -8 Reorder the terms: -13 + x = -8 Solving -13 + x = -8 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -8 + 13 Combine like terms: -13 + 13 = 0 0 + x = -8 + 13 x = -8 + 13 Combine like terms: -8 + 13 = 5 x = 5 Simplifying x = 5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {21, 5}

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