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Simplifying 5x2 + 10x + -14 = 20 Reorder the terms: -14 + 10x + 5x2 = 20 Solving -14 + 10x + 5x2 = 20 Solving for variable 'x'. Reorder the terms: -14 + -20 + 10x + 5x2 = 20 + -20 Combine like terms: -14 + -20 = -34 -34 + 10x + 5x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -34 + 10x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6.8 + 2x + x2 = 0 Move the constant term to the right: Add '6.8' to each side of the equation. -6.8 + 2x + 6.8 + x2 = 0 + 6.8 Reorder the terms: -6.8 + 6.8 + 2x + x2 = 0 + 6.8 Combine like terms: -6.8 + 6.8 = 0.0 0.0 + 2x + x2 = 0 + 6.8 2x + x2 = 0 + 6.8 Combine like terms: 0 + 6.8 = 6.8 2x + x2 = 6.8 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 6.8 + 1 Reorder the terms: 1 + 2x + x2 = 6.8 + 1 Combine like terms: 6.8 + 1 = 7.8 1 + 2x + x2 = 7.8 Factor a perfect square on the left side: (x + 1)(x + 1) = 7.8 Calculate the square root of the right side: 2.792848009 Break this problem into two subproblems by setting (x + 1) equal to 2.792848009 and -2.792848009.Subproblem 1
x + 1 = 2.792848009 Simplifying x + 1 = 2.792848009 Reorder the terms: 1 + x = 2.792848009 Solving 1 + x = 2.792848009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.792848009 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.792848009 + -1 x = 2.792848009 + -1 Combine like terms: 2.792848009 + -1 = 1.792848009 x = 1.792848009 Simplifying x = 1.792848009Subproblem 2
x + 1 = -2.792848009 Simplifying x + 1 = -2.792848009 Reorder the terms: 1 + x = -2.792848009 Solving 1 + x = -2.792848009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.792848009 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.792848009 + -1 x = -2.792848009 + -1 Combine like terms: -2.792848009 + -1 = -3.792848009 x = -3.792848009 Simplifying x = -3.792848009Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.792848009, -3.792848009}
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