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Simplifying 5x2 + -3x + -72 = 0 Reorder the terms: -72 + -3x + 5x2 = 0 Solving -72 + -3x + 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 + -0.6x + x2 = 0 Move the constant term to the right: Add '14.4' to each side of the equation. -14.4 + -0.6x + 14.4 + x2 = 0 + 14.4 Reorder the terms: -14.4 + 14.4 + -0.6x + x2 = 0 + 14.4 Combine like terms: -14.4 + 14.4 = 0.0 0.0 + -0.6x + x2 = 0 + 14.4 -0.6x + x2 = 0 + 14.4 Combine like terms: 0 + 14.4 = 14.4 -0.6x + x2 = 14.4 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 14.4 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 14.4 + 0.09 Combine like terms: 14.4 + 0.09 = 14.49 0.09 + -0.6x + x2 = 14.49 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 14.49 Calculate the square root of the right side: 3.806573262 Break this problem into two subproblems by setting (x + -0.3) equal to 3.806573262 and -3.806573262.Subproblem 1
x + -0.3 = 3.806573262 Simplifying x + -0.3 = 3.806573262 Reorder the terms: -0.3 + x = 3.806573262 Solving -0.3 + x = 3.806573262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 3.806573262 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 3.806573262 + 0.3 x = 3.806573262 + 0.3 Combine like terms: 3.806573262 + 0.3 = 4.106573262 x = 4.106573262 Simplifying x = 4.106573262Subproblem 2
x + -0.3 = -3.806573262 Simplifying x + -0.3 = -3.806573262 Reorder the terms: -0.3 + x = -3.806573262 Solving -0.3 + x = -3.806573262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -3.806573262 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -3.806573262 + 0.3 x = -3.806573262 + 0.3 Combine like terms: -3.806573262 + 0.3 = -3.506573262 x = -3.506573262 Simplifying x = -3.506573262Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.106573262, -3.506573262}
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