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Simplifying 5x2 + -24x + -21 = 0 Reorder the terms: -21 + -24x + 5x2 = 0 Solving -21 + -24x + 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'. -4.2 + -4.8x + x2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + -4.8x + 4.2 + x2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + -4.8x + x2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + -4.8x + x2 = 0 + 4.2 -4.8x + x2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 -4.8x + x2 = 4.2 The x term is -4.8x. Take half its coefficient (-2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. -4.8x + 5.76 + x2 = 4.2 + 5.76 Reorder the terms: 5.76 + -4.8x + x2 = 4.2 + 5.76 Combine like terms: 4.2 + 5.76 = 9.96 5.76 + -4.8x + x2 = 9.96 Factor a perfect square on the left side: (x + -2.4)(x + -2.4) = 9.96 Calculate the square root of the right side: 3.155946768 Break this problem into two subproblems by setting (x + -2.4) equal to 3.155946768 and -3.155946768.Subproblem 1
x + -2.4 = 3.155946768 Simplifying x + -2.4 = 3.155946768 Reorder the terms: -2.4 + x = 3.155946768 Solving -2.4 + x = 3.155946768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + x = 3.155946768 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = 3.155946768 + 2.4 x = 3.155946768 + 2.4 Combine like terms: 3.155946768 + 2.4 = 5.555946768 x = 5.555946768 Simplifying x = 5.555946768Subproblem 2
x + -2.4 = -3.155946768 Simplifying x + -2.4 = -3.155946768 Reorder the terms: -2.4 + x = -3.155946768 Solving -2.4 + x = -3.155946768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + x = -3.155946768 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = -3.155946768 + 2.4 x = -3.155946768 + 2.4 Combine like terms: -3.155946768 + 2.4 = -0.755946768 x = -0.755946768 Simplifying x = -0.755946768Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.555946768, -0.755946768}
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