(16-x)*(14-x)=187

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Solution for (16-x)*(14-x)=187 equation:


Simplifying
(16 + -1x)(14 + -1x) = 187

Multiply (16 + -1x) * (14 + -1x)
(16(14 + -1x) + -1x * (14 + -1x)) = 187
((14 * 16 + -1x * 16) + -1x * (14 + -1x)) = 187
((224 + -16x) + -1x * (14 + -1x)) = 187
(224 + -16x + (14 * -1x + -1x * -1x)) = 187
(224 + -16x + (-14x + 1x2)) = 187

Combine like terms: -16x + -14x = -30x
(224 + -30x + 1x2) = 187

Solving
224 + -30x + 1x2 = 187

Solving for variable 'x'.

Reorder the terms:
224 + -187 + -30x + 1x2 = 187 + -187

Combine like terms: 224 + -187 = 37
37 + -30x + 1x2 = 187 + -187

Combine like terms: 187 + -187 = 0
37 + -30x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-37' to each side of the equation.
37 + -30x + -37 + x2 = 0 + -37

Reorder the terms:
37 + -37 + -30x + x2 = 0 + -37

Combine like terms: 37 + -37 = 0
0 + -30x + x2 = 0 + -37
-30x + x2 = 0 + -37

Combine like terms: 0 + -37 = -37
-30x + x2 = -37

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = -37 + 225

Reorder the terms:
225 + -30x + x2 = -37 + 225

Combine like terms: -37 + 225 = 188
225 + -30x + x2 = 188

Factor a perfect square on the left side:
(x + -15)(x + -15) = 188

Calculate the square root of the right side: 13.711309201

Break this problem into two subproblems by setting 
(x + -15) equal to 13.711309201 and -13.711309201.

Subproblem 1

x + -15 = 13.711309201 Simplifying x + -15 = 13.711309201 Reorder the terms: -15 + x = 13.711309201 Solving -15 + x = 13.711309201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 13.711309201 + 15 Combine like terms: -15 + 15 = 0 0 + x = 13.711309201 + 15 x = 13.711309201 + 15 Combine like terms: 13.711309201 + 15 = 28.711309201 x = 28.711309201 Simplifying x = 28.711309201

Subproblem 2

x + -15 = -13.711309201 Simplifying x + -15 = -13.711309201 Reorder the terms: -15 + x = -13.711309201 Solving -15 + x = -13.711309201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -13.711309201 + 15 Combine like terms: -15 + 15 = 0 0 + x = -13.711309201 + 15 x = -13.711309201 + 15 Combine like terms: -13.711309201 + 15 = 1.288690799 x = 1.288690799 Simplifying x = 1.288690799

Solution

The solution to the problem is based on the solutions from the subproblems. x = {28.711309201, 1.288690799}

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