24x^2-14x-5=4x^2+8x+3

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Solution for 24x^2-14x-5=4x^2+8x+3 equation:


Simplifying
24x2 + -14x + -5 = 4x2 + 8x + 3

Reorder the terms:
-5 + -14x + 24x2 = 4x2 + 8x + 3

Reorder the terms:
-5 + -14x + 24x2 = 3 + 8x + 4x2

Solving
-5 + -14x + 24x2 = 3 + 8x + 4x2

Solving for variable 'x'.

Reorder the terms:
-5 + -3 + -14x + -8x + 24x2 + -4x2 = 3 + 8x + 4x2 + -3 + -8x + -4x2

Combine like terms: -5 + -3 = -8
-8 + -14x + -8x + 24x2 + -4x2 = 3 + 8x + 4x2 + -3 + -8x + -4x2

Combine like terms: -14x + -8x = -22x
-8 + -22x + 24x2 + -4x2 = 3 + 8x + 4x2 + -3 + -8x + -4x2

Combine like terms: 24x2 + -4x2 = 20x2
-8 + -22x + 20x2 = 3 + 8x + 4x2 + -3 + -8x + -4x2

Reorder the terms:
-8 + -22x + 20x2 = 3 + -3 + 8x + -8x + 4x2 + -4x2

Combine like terms: 3 + -3 = 0
-8 + -22x + 20x2 = 0 + 8x + -8x + 4x2 + -4x2
-8 + -22x + 20x2 = 8x + -8x + 4x2 + -4x2

Combine like terms: 8x + -8x = 0
-8 + -22x + 20x2 = 0 + 4x2 + -4x2
-8 + -22x + 20x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-8 + -22x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -11x + 10x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-4 + -11x + 10x2)' equal to zero and attempt to solve: Simplifying -4 + -11x + 10x2 = 0 Solving -4 + -11x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.4 + -1.1x + x2 = 0.0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -1.1x + 0.4 + x2 = 0.0 + 0.4 Reorder the terms: -0.4 + 0.4 + -1.1x + x2 = 0.0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -1.1x + x2 = 0.0 + 0.4 -1.1x + x2 = 0.0 + 0.4 Combine like terms: 0.0 + 0.4 = 0.4 -1.1x + x2 = 0.4 The x term is -1.1x. Take half its coefficient (-0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. -1.1x + 0.3025 + x2 = 0.4 + 0.3025 Reorder the terms: 0.3025 + -1.1x + x2 = 0.4 + 0.3025 Combine like terms: 0.4 + 0.3025 = 0.7025 0.3025 + -1.1x + x2 = 0.7025 Factor a perfect square on the left side: (x + -0.55)(x + -0.55) = 0.7025 Calculate the square root of the right side: 0.838152731 Break this problem into two subproblems by setting (x + -0.55) equal to 0.838152731 and -0.838152731.

Subproblem 1

x + -0.55 = 0.838152731 Simplifying x + -0.55 = 0.838152731 Reorder the terms: -0.55 + x = 0.838152731 Solving -0.55 + x = 0.838152731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + x = 0.838152731 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = 0.838152731 + 0.55 x = 0.838152731 + 0.55 Combine like terms: 0.838152731 + 0.55 = 1.388152731 x = 1.388152731 Simplifying x = 1.388152731

Subproblem 2

x + -0.55 = -0.838152731 Simplifying x + -0.55 = -0.838152731 Reorder the terms: -0.55 + x = -0.838152731 Solving -0.55 + x = -0.838152731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + x = -0.838152731 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = -0.838152731 + 0.55 x = -0.838152731 + 0.55 Combine like terms: -0.838152731 + 0.55 = -0.288152731 x = -0.288152731 Simplifying x = -0.288152731

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.388152731, -0.288152731}

Solution

x = {1.388152731, -0.288152731}

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