2x+3=x^2-10x-5 - Solution

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2x+3=x^2-10x-5

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Solution for 2x+3=x^2-10x-5 equation:

Simplifying 2x + 3 = x2 + -10x + -5 Reorder the terms: 3 + 2x = x2 + -10x + -5 Reorder the terms: 3 + 2x = -5 + -10x + x2 Solving 3 + 2x = -5 + -10x + x2 Solving for variable 'x'. Reorder the terms: 3 + 5 + 2x + 10x + -1x2 = -5 + -10x + x2 + 5 + 10x + -1x2 Combine like terms: 3 + 5 = 8 8 + 2x + 10x + -1x2 = -5 + -10x + x2 + 5 + 10x + -1x2 Combine like terms: 2x + 10x = 12x 8 + 12x + -1x2 = -5 + -10x + x2 + 5 + 10x + -1x2 Reorder the terms: 8 + 12x + -1x2 = -5 + 5 + -10x + 10x + x2 + -1x2 Combine like terms: -5 + 5 = 0 8 + 12x + -1x2 = 0 + -10x + 10x + x2 + -1x2 8 + 12x + -1x2 = -10x + 10x + x2 + -1x2 Combine like terms: -10x + 10x = 0 8 + 12x + -1x2 = 0 + x2 + -1x2 8 + 12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 8 + 12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + -12x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -12x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -12x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -12x + x2 = 0 + 8 -12x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -12x + x2 = 8 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 8 + 36 Reorder the terms: 36 + -12x + x2 = 8 + 36 Combine like terms: 8 + 36 = 44 36 + -12x + x2 = 44 Factor a perfect square on the left side: (x + -6)(x + -6) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (x + -6) equal to 6.633249581 and -6.633249581.

Subproblem 1

x + -6 = 6.633249581 Simplifying x + -6 = 6.633249581 Reorder the terms: -6 + x = 6.633249581 Solving -6 + x = 6.633249581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 6.633249581 + 6 Combine like terms: -6 + 6 = 0 0 + x = 6.633249581 + 6 x = 6.633249581 + 6 Combine like terms: 6.633249581 + 6 = 12.633249581 x = 12.633249581 Simplifying x = 12.633249581

Subproblem 2

x + -6 = -6.633249581 Simplifying x + -6 = -6.633249581 Reorder the terms: -6 + x = -6.633249581 Solving -6 + x = -6.633249581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -6.633249581 + 6 Combine like terms: -6 + 6 = 0 0 + x = -6.633249581 + 6 x = -6.633249581 + 6 Combine like terms: -6.633249581 + 6 = -0.633249581 x = -0.633249581 Simplifying x = -0.633249581

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.633249581, -0.633249581}

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