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Simplifying 5x2 + 21x + -270 = 0 Reorder the terms: -270 + 21x + 5x2 = 0 Solving -270 + 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'. -54 + 4.2x + x2 = 0 Move the constant term to the right: Add '54' to each side of the equation. -54 + 4.2x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + 4.2x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 4.2x + x2 = 0 + 54 4.2x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 4.2x + x2 = 54 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 = 54 + 4.41 Reorder the terms: 4.41 + 4.2x + x2 = 54 + 4.41 Combine like terms: 54 + 4.41 = 58.41 4.41 + 4.2x + x2 = 58.41 Factor a perfect square on the left side: (x + 2.1)(x + 2.1) = 58.41 Calculate the square root of the right side: 7.642643522 Break this problem into two subproblems by setting (x + 2.1) equal to 7.642643522 and -7.642643522.Subproblem 1
x + 2.1 = 7.642643522 Simplifying x + 2.1 = 7.642643522 Reorder the terms: 2.1 + x = 7.642643522 Solving 2.1 + x = 7.642643522 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 = 7.642643522 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + x = 7.642643522 + -2.1 x = 7.642643522 + -2.1 Combine like terms: 7.642643522 + -2.1 = 5.542643522 x = 5.542643522 Simplifying x = 5.542643522Subproblem 2
x + 2.1 = -7.642643522 Simplifying x + 2.1 = -7.642643522 Reorder the terms: 2.1 + x = -7.642643522 Solving 2.1 + x = -7.642643522 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 = -7.642643522 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + x = -7.642643522 + -2.1 x = -7.642643522 + -2.1 Combine like terms: -7.642643522 + -2.1 = -9.742643522 x = -9.742643522 Simplifying x = -9.742643522Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.542643522, -9.742643522}
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