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Simplifying 5x2 + 21x + -6 = 0 Reorder the terms: -6 + 21x + 5x2 = 0 Solving -6 + 21x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + 4.2x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 4.2x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 4.2x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 4.2x + x2 = 0 + 1.2 4.2x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 4.2x + x2 = 1.2 The x term is 4.2x. Take half its coefficient (2.1). Square it (4.41) and add it to both sides. Add '4.41' to each side of the equation. 4.2x + 4.41 + x2 = 1.2 + 4.41 Reorder the terms: 4.41 + 4.2x + x2 = 1.2 + 4.41 Combine like terms: 1.2 + 4.41 = 5.61 4.41 + 4.2x + x2 = 5.61 Factor a perfect square on the left side: (x + 2.1)(x + 2.1) = 5.61 Calculate the square root of the right side: 2.368543856 Break this problem into two subproblems by setting (x + 2.1) equal to 2.368543856 and -2.368543856.Subproblem 1
x + 2.1 = 2.368543856 Simplifying x + 2.1 = 2.368543856 Reorder the terms: 2.1 + x = 2.368543856 Solving 2.1 + x = 2.368543856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + x = 2.368543856 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + x = 2.368543856 + -2.1 x = 2.368543856 + -2.1 Combine like terms: 2.368543856 + -2.1 = 0.268543856 x = 0.268543856 Simplifying x = 0.268543856Subproblem 2
x + 2.1 = -2.368543856 Simplifying x + 2.1 = -2.368543856 Reorder the terms: 2.1 + x = -2.368543856 Solving 2.1 + x = -2.368543856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + x = -2.368543856 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + x = -2.368543856 + -2.1 x = -2.368543856 + -2.1 Combine like terms: -2.368543856 + -2.1 = -4.468543856 x = -4.468543856 Simplifying x = -4.468543856Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.268543856, -4.468543856}
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