(x-14)(x+.5)=

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Solution for (x-14)(x+.5)= equation:


Simplifying
(x + -14)(x + 0.5) = 0

Reorder the terms:
(-14 + x)(x + 0.5) = 0

Reorder the terms:
(-14 + x)(0.5 + x) = 0

Multiply (-14 + x) * (0.5 + x)
(-14(0.5 + x) + x(0.5 + x)) = 0
((0.5 * -14 + x * -14) + x(0.5 + x)) = 0
((-7 + -14x) + x(0.5 + x)) = 0
(-7 + -14x + (0.5 * x + x * x)) = 0
(-7 + -14x + (0.5x + x2)) = 0

Combine like terms: -14x + 0.5x = -13.5x
(-7 + -13.5x + x2) = 0

Solving
-7 + -13.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -13.5x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -13.5x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -13.5x + x2 = 0 + 7
-13.5x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-13.5x + x2 = 7

The x term is -13.5x.  Take half its coefficient (-6.75).
Square it (45.5625) and add it to both sides.

Add '45.5625' to each side of the equation.
-13.5x + 45.5625 + x2 = 7 + 45.5625

Reorder the terms:
45.5625 + -13.5x + x2 = 7 + 45.5625

Combine like terms: 7 + 45.5625 = 52.5625
45.5625 + -13.5x + x2 = 52.5625

Factor a perfect square on the left side:
(x + -6.75)(x + -6.75) = 52.5625

Calculate the square root of the right side: 7.25

Break this problem into two subproblems by setting 
(x + -6.75) equal to 7.25 and -7.25.

Subproblem 1

x + -6.75 = 7.25 Simplifying x + -6.75 = 7.25 Reorder the terms: -6.75 + x = 7.25 Solving -6.75 + x = 7.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + x = 7.25 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = 7.25 + 6.75 x = 7.25 + 6.75 Combine like terms: 7.25 + 6.75 = 14 x = 14 Simplifying x = 14

Subproblem 2

x + -6.75 = -7.25 Simplifying x + -6.75 = -7.25 Reorder the terms: -6.75 + x = -7.25 Solving -6.75 + x = -7.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + x = -7.25 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = -7.25 + 6.75 x = -7.25 + 6.75 Combine like terms: -7.25 + 6.75 = -0.5 x = -0.5 Simplifying x = -0.5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14, -0.5}

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