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Simplifying 2x2 + 10x + -21 = 0 Reorder the terms: -21 + 10x + 2x2 = 0 Solving -21 + 10x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10.5 + 5x + x2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + 5x + 10.5 + x2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + 5x + x2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + 5x + x2 = 0 + 10.5 5x + x2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 5x + x2 = 10.5 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 = 10.5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 10.5 + 6.25 Combine like terms: 10.5 + 6.25 = 16.75 6.25 + 5x + x2 = 16.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 16.75 Calculate the square root of the right side: 4.092676386 Break this problem into two subproblems by setting (x + 2.5) equal to 4.092676386 and -4.092676386.Subproblem 1
x + 2.5 = 4.092676386 Simplifying x + 2.5 = 4.092676386 Reorder the terms: 2.5 + x = 4.092676386 Solving 2.5 + x = 4.092676386 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 = 4.092676386 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 4.092676386 + -2.5 x = 4.092676386 + -2.5 Combine like terms: 4.092676386 + -2.5 = 1.592676386 x = 1.592676386 Simplifying x = 1.592676386Subproblem 2
x + 2.5 = -4.092676386 Simplifying x + 2.5 = -4.092676386 Reorder the terms: 2.5 + x = -4.092676386 Solving 2.5 + x = -4.092676386 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 = -4.092676386 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -4.092676386 + -2.5 x = -4.092676386 + -2.5 Combine like terms: -4.092676386 + -2.5 = -6.592676386 x = -6.592676386 Simplifying x = -6.592676386Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.592676386, -6.592676386}
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