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Simplifying 5x2 + 16x + -95 = 0 Reorder the terms: -95 + 16x + 5x2 = 0 Solving -95 + 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'. -19 + 3.2x + x2 = 0 Move the constant term to the right: Add '19' to each side of the equation. -19 + 3.2x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + 3.2x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 3.2x + x2 = 0 + 19 3.2x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 3.2x + x2 = 19 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 = 19 + 2.56 Reorder the terms: 2.56 + 3.2x + x2 = 19 + 2.56 Combine like terms: 19 + 2.56 = 21.56 2.56 + 3.2x + x2 = 21.56 Factor a perfect square on the left side: (x + 1.6)(x + 1.6) = 21.56 Calculate the square root of the right side: 4.643274706 Break this problem into two subproblems by setting (x + 1.6) equal to 4.643274706 and -4.643274706.Subproblem 1
x + 1.6 = 4.643274706 Simplifying x + 1.6 = 4.643274706 Reorder the terms: 1.6 + x = 4.643274706 Solving 1.6 + x = 4.643274706 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 = 4.643274706 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = 4.643274706 + -1.6 x = 4.643274706 + -1.6 Combine like terms: 4.643274706 + -1.6 = 3.043274706 x = 3.043274706 Simplifying x = 3.043274706Subproblem 2
x + 1.6 = -4.643274706 Simplifying x + 1.6 = -4.643274706 Reorder the terms: 1.6 + x = -4.643274706 Solving 1.6 + x = -4.643274706 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 = -4.643274706 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = -4.643274706 + -1.6 x = -4.643274706 + -1.6 Combine like terms: -4.643274706 + -1.6 = -6.243274706 x = -6.243274706 Simplifying x = -6.243274706Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.043274706, -6.243274706}
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