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Simplifying 5x2 + 12x + -2160 = 0 Reorder the terms: -2160 + 12x + 5x2 = 0 Solving -2160 + 12x + 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'. -432 + 2.4x + x2 = 0 Move the constant term to the right: Add '432' to each side of the equation. -432 + 2.4x + 432 + x2 = 0 + 432 Reorder the terms: -432 + 432 + 2.4x + x2 = 0 + 432 Combine like terms: -432 + 432 = 0 0 + 2.4x + x2 = 0 + 432 2.4x + x2 = 0 + 432 Combine like terms: 0 + 432 = 432 2.4x + x2 = 432 The x term is 2.4x. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4x + 1.44 + x2 = 432 + 1.44 Reorder the terms: 1.44 + 2.4x + x2 = 432 + 1.44 Combine like terms: 432 + 1.44 = 433.44 1.44 + 2.4x + x2 = 433.44 Factor a perfect square on the left side: (x + 1.2)(x + 1.2) = 433.44 Calculate the square root of the right side: 20.819221887 Break this problem into two subproblems by setting (x + 1.2) equal to 20.819221887 and -20.819221887.Subproblem 1
x + 1.2 = 20.819221887 Simplifying x + 1.2 = 20.819221887 Reorder the terms: 1.2 + x = 20.819221887 Solving 1.2 + x = 20.819221887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = 20.819221887 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 20.819221887 + -1.2 x = 20.819221887 + -1.2 Combine like terms: 20.819221887 + -1.2 = 19.619221887 x = 19.619221887 Simplifying x = 19.619221887Subproblem 2
x + 1.2 = -20.819221887 Simplifying x + 1.2 = -20.819221887 Reorder the terms: 1.2 + x = -20.819221887 Solving 1.2 + x = -20.819221887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = -20.819221887 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -20.819221887 + -1.2 x = -20.819221887 + -1.2 Combine like terms: -20.819221887 + -1.2 = -22.019221887 x = -22.019221887 Simplifying x = -22.019221887Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.619221887, -22.019221887}
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