# 15=-2x*x+100*x

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## Solution for 15=-2x*x+100*x equation:

Simplifying
15 = -2x * x + 100x
Multiply x * x
15 = -2x2 + 100x
Reorder the terms:
15 = 100x + -2x2
Solving
15 = 100x + -2x2
Solving for variable 'x'.
Reorder the terms:
15 + -100x + 2x2 = 100x + -100x + -2x2 + 2x2
Combine like terms: 100x + -100x = 0
15 + -100x + 2x2 = 0 + -2x2 + 2x2
15 + -100x + 2x2 = -2x2 + 2x2
Combine like terms: -2x2 + 2x2 = 0
15 + -100x + 2x2 = 0
Begin completing the square. Divide all terms by
2 the coefficient of the squared term:
Divide each side by '2'.
7.5 + -50x + x2 = 0
Move the constant term to the right:
Add '-7.5' to each side of the equation.
7.5 + -50x + -7.5 + x2 = 0 + -7.5
Reorder the terms:
7.5 + -7.5 + -50x + x2 = 0 + -7.5
Combine like terms: 7.5 + -7.5 = 0.0
0.0 + -50x + x2 = 0 + -7.5
-50x + x2 = 0 + -7.5
Combine like terms: 0 + -7.5 = -7.5
-50x + x2 = -7.5
The x term is -50x. Take half its coefficient (-25).
Square it (625) and add it to both sides.
Add '625' to each side of the equation.
-50x + 625 + x2 = -7.5 + 625
Reorder the terms:
625 + -50x + x2 = -7.5 + 625
Combine like terms: -7.5 + 625 = 617.5
625 + -50x + x2 = 617.5
Factor a perfect square on the left side:
(x + -25)(x + -25) = 617.5
Calculate the square root of the right side: 24.84954728
Break this problem into two subproblems by setting
(x + -25) equal to 24.84954728 and -24.84954728.
Subproblem 1x + -25 = 24.84954728
Simplifying
x + -25 = 24.84954728
Reorder the terms:
-25 + x = 24.84954728
Solving
-25 + x = 24.84954728
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '25' to each side of the equation.
-25 + 25 + x = 24.84954728 + 25
Combine like terms: -25 + 25 = 0
0 + x = 24.84954728 + 25
x = 24.84954728 + 25
Combine like terms: 24.84954728 + 25 = 49.84954728
x = 49.84954728
Simplifying
x = 49.84954728
Subproblem 2x + -25 = -24.84954728
Simplifying
x + -25 = -24.84954728
Reorder the terms:
-25 + x = -24.84954728
Solving
-25 + x = -24.84954728
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '25' to each side of the equation.
-25 + 25 + x = -24.84954728 + 25
Combine like terms: -25 + 25 = 0
0 + x = -24.84954728 + 25
x = -24.84954728 + 25
Combine like terms: -24.84954728 + 25 = 0.15045272
x = 0.15045272
Simplifying
x = 0.15045272
SolutionThe solution to the problem is based on the solutions
from the subproblems.
x = {49.84954728, 0.15045272}`