1.5=-0.0001x^2+0.0542x+1.1784

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Solution for 1.5=-0.0001x^2+0.0542x+1.1784 equation:


Simplifying
1.5 = -0.0001x2 + 0.0542x + 1.1784

Reorder the terms:
1.5 = 1.1784 + 0.0542x + -0.0001x2

Solving
1.5 = 1.1784 + 0.0542x + -0.0001x2

Solving for variable 'x'.

Combine like terms: 1.5 + -1.1784 = 0.3216
0.3216 + -0.0542x + 0.0001x2 = 1.1784 + 0.0542x + -0.0001x2 + -1.1784 + -0.0542x + 0.0001x2

Reorder the terms:
0.3216 + -0.0542x + 0.0001x2 = 1.1784 + -1.1784 + 0.0542x + -0.0542x + -0.0001x2 + 0.0001x2

Combine like terms: 1.1784 + -1.1784 = 0.0000
0.3216 + -0.0542x + 0.0001x2 = 0.0000 + 0.0542x + -0.0542x + -0.0001x2 + 0.0001x2
0.3216 + -0.0542x + 0.0001x2 = 0.0542x + -0.0542x + -0.0001x2 + 0.0001x2

Combine like terms: 0.0542x + -0.0542x = 0.0000
0.3216 + -0.0542x + 0.0001x2 = 0.0000 + -0.0001x2 + 0.0001x2
0.3216 + -0.0542x + 0.0001x2 = -0.0001x2 + 0.0001x2

Combine like terms: -0.0001x2 + 0.0001x2 = 0.0000
0.3216 + -0.0542x + 0.0001x2 = 0.0000

Begin completing the square.  Divide all terms by
0.0001 the coefficient of the squared term: 

Divide each side by '0.0001'.
3216 + -542x + x2 = 0

Move the constant term to the right:

Add '-3216' to each side of the equation.
3216 + -542x + -3216 + x2 = 0 + -3216

Reorder the terms:
3216 + -3216 + -542x + x2 = 0 + -3216

Combine like terms: 3216 + -3216 = 0
0 + -542x + x2 = 0 + -3216
-542x + x2 = 0 + -3216

Combine like terms: 0 + -3216 = -3216
-542x + x2 = -3216

The x term is -542x.  Take half its coefficient (-271).
Square it (73441) and add it to both sides.

Add '73441' to each side of the equation.
-542x + 73441 + x2 = -3216 + 73441

Reorder the terms:
73441 + -542x + x2 = -3216 + 73441

Combine like terms: -3216 + 73441 = 70225
73441 + -542x + x2 = 70225

Factor a perfect square on the left side:
(x + -271)(x + -271) = 70225

Calculate the square root of the right side: 265

Break this problem into two subproblems by setting 
(x + -271) equal to 265 and -265.

Subproblem 1

x + -271 = 265 Simplifying x + -271 = 265 Reorder the terms: -271 + x = 265 Solving -271 + x = 265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '271' to each side of the equation. -271 + 271 + x = 265 + 271 Combine like terms: -271 + 271 = 0 0 + x = 265 + 271 x = 265 + 271 Combine like terms: 265 + 271 = 536 x = 536 Simplifying x = 536

Subproblem 2

x + -271 = -265 Simplifying x + -271 = -265 Reorder the terms: -271 + x = -265 Solving -271 + x = -265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '271' to each side of the equation. -271 + 271 + x = -265 + 271 Combine like terms: -271 + 271 = 0 0 + x = -265 + 271 x = -265 + 271 Combine like terms: -265 + 271 = 6 x = 6 Simplifying x = 6

Solution

The solution to the problem is based on the solutions from the subproblems. x = {536, 6}

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