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Simplifying 5x2 + 16x + -19 = 0 Reorder the terms: -19 + 16x + 5x2 = 0 Solving -19 + 16x + 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'. -3.8 + 3.2x + x2 = 0 Move the constant term to the right: Add '3.8' to each side of the equation. -3.8 + 3.2x + 3.8 + x2 = 0 + 3.8 Reorder the terms: -3.8 + 3.8 + 3.2x + x2 = 0 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + 3.2x + x2 = 0 + 3.8 3.2x + x2 = 0 + 3.8 Combine like terms: 0 + 3.8 = 3.8 3.2x + x2 = 3.8 The x term is 3.2x. Take half its coefficient (1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. 3.2x + 2.56 + x2 = 3.8 + 2.56 Reorder the terms: 2.56 + 3.2x + x2 = 3.8 + 2.56 Combine like terms: 3.8 + 2.56 = 6.36 2.56 + 3.2x + x2 = 6.36 Factor a perfect square on the left side: (x + 1.6)(x + 1.6) = 6.36 Calculate the square root of the right side: 2.521904043 Break this problem into two subproblems by setting (x + 1.6) equal to 2.521904043 and -2.521904043.Subproblem 1
x + 1.6 = 2.521904043 Simplifying x + 1.6 = 2.521904043 Reorder the terms: 1.6 + x = 2.521904043 Solving 1.6 + x = 2.521904043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = 2.521904043 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = 2.521904043 + -1.6 x = 2.521904043 + -1.6 Combine like terms: 2.521904043 + -1.6 = 0.921904043 x = 0.921904043 Simplifying x = 0.921904043Subproblem 2
x + 1.6 = -2.521904043 Simplifying x + 1.6 = -2.521904043 Reorder the terms: 1.6 + x = -2.521904043 Solving 1.6 + x = -2.521904043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = -2.521904043 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = -2.521904043 + -1.6 x = -2.521904043 + -1.6 Combine like terms: -2.521904043 + -1.6 = -4.121904043 x = -4.121904043 Simplifying x = -4.121904043Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.921904043, -4.121904043}
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