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Simplifying 5x2 + -24x + -37 = 0 Reorder the terms: -37 + -24x + 5x2 = 0 Solving -37 + -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'. -7.4 + -4.8x + x2 = 0 Move the constant term to the right: Add '7.4' to each side of the equation. -7.4 + -4.8x + 7.4 + x2 = 0 + 7.4 Reorder the terms: -7.4 + 7.4 + -4.8x + x2 = 0 + 7.4 Combine like terms: -7.4 + 7.4 = 0.0 0.0 + -4.8x + x2 = 0 + 7.4 -4.8x + x2 = 0 + 7.4 Combine like terms: 0 + 7.4 = 7.4 -4.8x + x2 = 7.4 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 = 7.4 + 5.76 Reorder the terms: 5.76 + -4.8x + x2 = 7.4 + 5.76 Combine like terms: 7.4 + 5.76 = 13.16 5.76 + -4.8x + x2 = 13.16 Factor a perfect square on the left side: (x + -2.4)(x + -2.4) = 13.16 Calculate the square root of the right side: 3.627671429 Break this problem into two subproblems by setting (x + -2.4) equal to 3.627671429 and -3.627671429.Subproblem 1
x + -2.4 = 3.627671429 Simplifying x + -2.4 = 3.627671429 Reorder the terms: -2.4 + x = 3.627671429 Solving -2.4 + x = 3.627671429 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 = 3.627671429 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = 3.627671429 + 2.4 x = 3.627671429 + 2.4 Combine like terms: 3.627671429 + 2.4 = 6.027671429 x = 6.027671429 Simplifying x = 6.027671429Subproblem 2
x + -2.4 = -3.627671429 Simplifying x + -2.4 = -3.627671429 Reorder the terms: -2.4 + x = -3.627671429 Solving -2.4 + x = -3.627671429 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 = -3.627671429 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = -3.627671429 + 2.4 x = -3.627671429 + 2.4 Combine like terms: -3.627671429 + 2.4 = -1.227671429 x = -1.227671429 Simplifying x = -1.227671429Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.027671429, -1.227671429}
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