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Simplifying -5x2 + 48x + -30 = 0 Reorder the terms: -30 + 48x + -5x2 = 0 Solving -30 + 48x + -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'. 6 + -9.6x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -9.6x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -9.6x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -9.6x + x2 = 0 + -6 -9.6x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -9.6x + x2 = -6 The x term is -9.6x. Take half its coefficient (-4.8). Square it (23.04) and add it to both sides. Add '23.04' to each side of the equation. -9.6x + 23.04 + x2 = -6 + 23.04 Reorder the terms: 23.04 + -9.6x + x2 = -6 + 23.04 Combine like terms: -6 + 23.04 = 17.04 23.04 + -9.6x + x2 = 17.04 Factor a perfect square on the left side: (x + -4.8)(x + -4.8) = 17.04 Calculate the square root of the right side: 4.127953488 Break this problem into two subproblems by setting (x + -4.8) equal to 4.127953488 and -4.127953488.Subproblem 1
x + -4.8 = 4.127953488 Simplifying x + -4.8 = 4.127953488 Reorder the terms: -4.8 + x = 4.127953488 Solving -4.8 + x = 4.127953488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.8' to each side of the equation. -4.8 + 4.8 + x = 4.127953488 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + x = 4.127953488 + 4.8 x = 4.127953488 + 4.8 Combine like terms: 4.127953488 + 4.8 = 8.927953488 x = 8.927953488 Simplifying x = 8.927953488Subproblem 2
x + -4.8 = -4.127953488 Simplifying x + -4.8 = -4.127953488 Reorder the terms: -4.8 + x = -4.127953488 Solving -4.8 + x = -4.127953488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.8' to each side of the equation. -4.8 + 4.8 + x = -4.127953488 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + x = -4.127953488 + 4.8 x = -4.127953488 + 4.8 Combine like terms: -4.127953488 + 4.8 = 0.672046512 x = 0.672046512 Simplifying x = 0.672046512Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.927953488, 0.672046512}
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