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Simplifying 5x2 + -21x + -72 = 0 Reorder the terms: -72 + -21x + 5x2 = 0 Solving -72 + -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'. -14.4 + -4.2x + x2 = 0 Move the constant term to the right: Add '14.4' to each side of the equation. -14.4 + -4.2x + 14.4 + x2 = 0 + 14.4 Reorder the terms: -14.4 + 14.4 + -4.2x + x2 = 0 + 14.4 Combine like terms: -14.4 + 14.4 = 0.0 0.0 + -4.2x + x2 = 0 + 14.4 -4.2x + x2 = 0 + 14.4 Combine like terms: 0 + 14.4 = 14.4 -4.2x + x2 = 14.4 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 = 14.4 + 4.41 Reorder the terms: 4.41 + -4.2x + x2 = 14.4 + 4.41 Combine like terms: 14.4 + 4.41 = 18.81 4.41 + -4.2x + x2 = 18.81 Factor a perfect square on the left side: (x + -2.1)(x + -2.1) = 18.81 Calculate the square root of the right side: 4.337049688 Break this problem into two subproblems by setting (x + -2.1) equal to 4.337049688 and -4.337049688.Subproblem 1
x + -2.1 = 4.337049688 Simplifying x + -2.1 = 4.337049688 Reorder the terms: -2.1 + x = 4.337049688 Solving -2.1 + x = 4.337049688 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 = 4.337049688 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + x = 4.337049688 + 2.1 x = 4.337049688 + 2.1 Combine like terms: 4.337049688 + 2.1 = 6.437049688 x = 6.437049688 Simplifying x = 6.437049688Subproblem 2
x + -2.1 = -4.337049688 Simplifying x + -2.1 = -4.337049688 Reorder the terms: -2.1 + x = -4.337049688 Solving -2.1 + x = -4.337049688 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 = -4.337049688 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + x = -4.337049688 + 2.1 x = -4.337049688 + 2.1 Combine like terms: -4.337049688 + 2.1 = -2.237049688 x = -2.237049688 Simplifying x = -2.237049688Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.437049688, -2.237049688}
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