8x(-152+x)=-96

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Solution for 8x(-152+x)=-96 equation:


Simplifying
8x(-152 + x) = -96
(-152 * 8x + x * 8x) = -96
(-1216x + 8x2) = -96

Solving
-1216x + 8x2 = -96

Solving for variable 'x'.

Reorder the terms:
96 + -1216x + 8x2 = -96 + 96

Combine like terms: -96 + 96 = 0
96 + -1216x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(12 + -152x + x2) = 0

Ignore the factor 8.

Subproblem 1

Set the factor '(12 + -152x + x2)' equal to zero and attempt to solve: Simplifying 12 + -152x + x2 = 0 Solving 12 + -152x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -152x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -152x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -152x + x2 = 0 + -12 -152x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -152x + x2 = -12 The x term is -152x. Take half its coefficient (-76). Square it (5776) and add it to both sides. Add '5776' to each side of the equation. -152x + 5776 + x2 = -12 + 5776 Reorder the terms: 5776 + -152x + x2 = -12 + 5776 Combine like terms: -12 + 5776 = 5764 5776 + -152x + x2 = 5764 Factor a perfect square on the left side: (x + -76)(x + -76) = 5764 Calculate the square root of the right side: 75.921011584 Break this problem into two subproblems by setting (x + -76) equal to 75.921011584 and -75.921011584.

Subproblem 1

x + -76 = 75.921011584 Simplifying x + -76 = 75.921011584 Reorder the terms: -76 + x = 75.921011584 Solving -76 + x = 75.921011584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '76' to each side of the equation. -76 + 76 + x = 75.921011584 + 76 Combine like terms: -76 + 76 = 0 0 + x = 75.921011584 + 76 x = 75.921011584 + 76 Combine like terms: 75.921011584 + 76 = 151.921011584 x = 151.921011584 Simplifying x = 151.921011584

Subproblem 2

x + -76 = -75.921011584 Simplifying x + -76 = -75.921011584 Reorder the terms: -76 + x = -75.921011584 Solving -76 + x = -75.921011584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '76' to each side of the equation. -76 + 76 + x = -75.921011584 + 76 Combine like terms: -76 + 76 = 0 0 + x = -75.921011584 + 76 x = -75.921011584 + 76 Combine like terms: -75.921011584 + 76 = 0.078988416 x = 0.078988416 Simplifying x = 0.078988416

Solution

The solution to the problem is based on the solutions from the subproblems. x = {151.921011584, 0.078988416}

Solution

x = {151.921011584, 0.078988416}

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