2x^2-30x+24=0

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Solution for 2x^2-30x+24=0 equation:


Simplifying
2x2 + -30x + 24 = 0

Reorder the terms:
24 + -30x + 2x2 = 0

Solving
24 + -30x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -15x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(12 + -15x + x2)' equal to zero and attempt to solve: Simplifying 12 + -15x + x2 = 0 Solving 12 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -15x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -15x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -15x + x2 = 0 + -12 -15x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -15x + x2 = -12 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -12 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -12 + 56.25 Combine like terms: -12 + 56.25 = 44.25 56.25 + -15x + x2 = 44.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (x + -7.5) equal to 6.652067348 and -6.652067348.

Subproblem 1

x + -7.5 = 6.652067348 Simplifying x + -7.5 = 6.652067348 Reorder the terms: -7.5 + x = 6.652067348 Solving -7.5 + x = 6.652067348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 6.652067348 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 6.652067348 + 7.5 x = 6.652067348 + 7.5 Combine like terms: 6.652067348 + 7.5 = 14.152067348 x = 14.152067348 Simplifying x = 14.152067348

Subproblem 2

x + -7.5 = -6.652067348 Simplifying x + -7.5 = -6.652067348 Reorder the terms: -7.5 + x = -6.652067348 Solving -7.5 + x = -6.652067348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -6.652067348 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -6.652067348 + 7.5 x = -6.652067348 + 7.5 Combine like terms: -6.652067348 + 7.5 = 0.847932652 x = 0.847932652 Simplifying x = 0.847932652

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.152067348, 0.847932652}

Solution

x = {14.152067348, 0.847932652}

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