10+80x-16x^2=28

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Solution for 10+80x-16x^2=28 equation:


Simplifying
10 + 80x + -16x2 = 28

Solving
10 + 80x + -16x2 = 28

Solving for variable 'x'.

Reorder the terms:
10 + -28 + 80x + -16x2 = 28 + -28

Combine like terms: 10 + -28 = -18
-18 + 80x + -16x2 = 28 + -28

Combine like terms: 28 + -28 = 0
-18 + 80x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 40x + -8x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-9 + 40x + -8x2)' equal to zero and attempt to solve: Simplifying -9 + 40x + -8x2 = 0 Solving -9 + 40x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 1.125 + -5x + x2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + -5x + -1.125 + x2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + -5x + x2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + -5x + x2 = 0 + -1.125 -5x + x2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 -5x + x2 = -1.125 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -1.125 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -1.125 + 6.25 Combine like terms: -1.125 + 6.25 = 5.125 6.25 + -5x + x2 = 5.125 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 5.125 Calculate the square root of the right side: 2.263846285 Break this problem into two subproblems by setting (x + -2.5) equal to 2.263846285 and -2.263846285.

Subproblem 1

x + -2.5 = 2.263846285 Simplifying x + -2.5 = 2.263846285 Reorder the terms: -2.5 + x = 2.263846285 Solving -2.5 + x = 2.263846285 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.263846285 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.263846285 + 2.5 x = 2.263846285 + 2.5 Combine like terms: 2.263846285 + 2.5 = 4.763846285 x = 4.763846285 Simplifying x = 4.763846285

Subproblem 2

x + -2.5 = -2.263846285 Simplifying x + -2.5 = -2.263846285 Reorder the terms: -2.5 + x = -2.263846285 Solving -2.5 + x = -2.263846285 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.263846285 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.263846285 + 2.5 x = -2.263846285 + 2.5 Combine like terms: -2.263846285 + 2.5 = 0.236153715 x = 0.236153715 Simplifying x = 0.236153715

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.763846285, 0.236153715}

Solution

x = {4.763846285, 0.236153715}

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