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Simplifying -5x2 + -21x + 30 = 0 Reorder the terms: 30 + -21x + -5x2 = 0 Solving 30 + -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'. -6 + 4.2x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 4.2x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 4.2x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 4.2x + x2 = 0 + 6 4.2x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 4.2x + x2 = 6 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 = 6 + 4.41 Reorder the terms: 4.41 + 4.2x + x2 = 6 + 4.41 Combine like terms: 6 + 4.41 = 10.41 4.41 + 4.2x + x2 = 10.41 Factor a perfect square on the left side: (x + 2.1)(x + 2.1) = 10.41 Calculate the square root of the right side: 3.226453161 Break this problem into two subproblems by setting (x + 2.1) equal to 3.226453161 and -3.226453161.Subproblem 1
x + 2.1 = 3.226453161 Simplifying x + 2.1 = 3.226453161 Reorder the terms: 2.1 + x = 3.226453161 Solving 2.1 + x = 3.226453161 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 = 3.226453161 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + x = 3.226453161 + -2.1 x = 3.226453161 + -2.1 Combine like terms: 3.226453161 + -2.1 = 1.126453161 x = 1.126453161 Simplifying x = 1.126453161Subproblem 2
x + 2.1 = -3.226453161 Simplifying x + 2.1 = -3.226453161 Reorder the terms: 2.1 + x = -3.226453161 Solving 2.1 + x = -3.226453161 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 = -3.226453161 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + x = -3.226453161 + -2.1 x = -3.226453161 + -2.1 Combine like terms: -3.226453161 + -2.1 = -5.326453161 x = -5.326453161 Simplifying x = -5.326453161Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.126453161, -5.326453161}
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