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Simplifying 2x2 + 21x + -6.9 = 0 Reorder the terms: -6.9 + 21x + 2x2 = 0 Solving -6.9 + 21x + 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'. -3.45 + 10.5x + x2 = 0 Move the constant term to the right: Add '3.45' to each side of the equation. -3.45 + 10.5x + 3.45 + x2 = 0 + 3.45 Reorder the terms: -3.45 + 3.45 + 10.5x + x2 = 0 + 3.45 Combine like terms: -3.45 + 3.45 = 0.00 0.00 + 10.5x + x2 = 0 + 3.45 10.5x + x2 = 0 + 3.45 Combine like terms: 0 + 3.45 = 3.45 10.5x + x2 = 3.45 The x term is 10.5x. Take half its coefficient (5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. 10.5x + 27.5625 + x2 = 3.45 + 27.5625 Reorder the terms: 27.5625 + 10.5x + x2 = 3.45 + 27.5625 Combine like terms: 3.45 + 27.5625 = 31.0125 27.5625 + 10.5x + x2 = 31.0125 Factor a perfect square on the left side: (x + 5.25)(x + 5.25) = 31.0125 Calculate the square root of the right side: 5.568886783 Break this problem into two subproblems by setting (x + 5.25) equal to 5.568886783 and -5.568886783.Subproblem 1
x + 5.25 = 5.568886783 Simplifying x + 5.25 = 5.568886783 Reorder the terms: 5.25 + x = 5.568886783 Solving 5.25 + x = 5.568886783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = 5.568886783 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 5.568886783 + -5.25 x = 5.568886783 + -5.25 Combine like terms: 5.568886783 + -5.25 = 0.318886783 x = 0.318886783 Simplifying x = 0.318886783Subproblem 2
x + 5.25 = -5.568886783 Simplifying x + 5.25 = -5.568886783 Reorder the terms: 5.25 + x = -5.568886783 Solving 5.25 + x = -5.568886783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = -5.568886783 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -5.568886783 + -5.25 x = -5.568886783 + -5.25 Combine like terms: -5.568886783 + -5.25 = -10.818886783 x = -10.818886783 Simplifying x = -10.818886783Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.318886783, -10.818886783}
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