-5d*10d-7d+8=

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Solution for -5d*10d-7d+8= equation:


Simplifying
-5d * 10d + -7d + 8 = 0

Reorder the terms for easier multiplication:
-5 * 10d * d + -7d + 8 = 0

Multiply -5 * 10
-50d * d + -7d + 8 = 0

Multiply d * d
-50d2 + -7d + 8 = 0

Reorder the terms:
8 + -7d + -50d2 = 0

Solving
8 + -7d + -50d2 = 0

Solving for variable 'd'.

Begin completing the square.  Divide all terms by
-50 the coefficient of the squared term: 

Divide each side by '-50'.
-0.16 + 0.14d + d2 = 0.0

Move the constant term to the right:

Add '0.16' to each side of the equation.
-0.16 + 0.14d + 0.16 + d2 = 0.0 + 0.16

Reorder the terms:
-0.16 + 0.16 + 0.14d + d2 = 0.0 + 0.16

Combine like terms: -0.16 + 0.16 = 0.00
0.00 + 0.14d + d2 = 0.0 + 0.16
0.14d + d2 = 0.0 + 0.16

Combine like terms: 0.0 + 0.16 = 0.16
0.14d + d2 = 0.16

The d term is 0.14d.  Take half its coefficient (0.07).
Square it (0.0049) and add it to both sides.

Add '0.0049' to each side of the equation.
0.14d + 0.0049 + d2 = 0.16 + 0.0049

Reorder the terms:
0.0049 + 0.14d + d2 = 0.16 + 0.0049

Combine like terms: 0.16 + 0.0049 = 0.1649
0.0049 + 0.14d + d2 = 0.1649

Factor a perfect square on the left side:
(d + 0.07)(d + 0.07) = 0.1649

Calculate the square root of the right side: 0.40607881

Break this problem into two subproblems by setting 
(d + 0.07) equal to 0.40607881 and -0.40607881.

Subproblem 1

d + 0.07 = 0.40607881 Simplifying d + 0.07 = 0.40607881 Reorder the terms: 0.07 + d = 0.40607881 Solving 0.07 + d = 0.40607881 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.07' to each side of the equation. 0.07 + -0.07 + d = 0.40607881 + -0.07 Combine like terms: 0.07 + -0.07 = 0.00 0.00 + d = 0.40607881 + -0.07 d = 0.40607881 + -0.07 Combine like terms: 0.40607881 + -0.07 = 0.33607881 d = 0.33607881 Simplifying d = 0.33607881

Subproblem 2

d + 0.07 = -0.40607881 Simplifying d + 0.07 = -0.40607881 Reorder the terms: 0.07 + d = -0.40607881 Solving 0.07 + d = -0.40607881 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.07' to each side of the equation. 0.07 + -0.07 + d = -0.40607881 + -0.07 Combine like terms: 0.07 + -0.07 = 0.00 0.00 + d = -0.40607881 + -0.07 d = -0.40607881 + -0.07 Combine like terms: -0.40607881 + -0.07 = -0.47607881 d = -0.47607881 Simplifying d = -0.47607881

Solution

The solution to the problem is based on the solutions from the subproblems. d = {0.33607881, -0.47607881}

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