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Simplifying 2x2 + 16x + -70 = -9 Reorder the terms: -70 + 16x + 2x2 = -9 Solving -70 + 16x + 2x2 = -9 Solving for variable 'x'. Reorder the terms: -70 + 9 + 16x + 2x2 = -9 + 9 Combine like terms: -70 + 9 = -61 -61 + 16x + 2x2 = -9 + 9 Combine like terms: -9 + 9 = 0 -61 + 16x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -30.5 + 8x + x2 = 0 Move the constant term to the right: Add '30.5' to each side of the equation. -30.5 + 8x + 30.5 + x2 = 0 + 30.5 Reorder the terms: -30.5 + 30.5 + 8x + x2 = 0 + 30.5 Combine like terms: -30.5 + 30.5 = 0.0 0.0 + 8x + x2 = 0 + 30.5 8x + x2 = 0 + 30.5 Combine like terms: 0 + 30.5 = 30.5 8x + x2 = 30.5 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 30.5 + 16 Reorder the terms: 16 + 8x + x2 = 30.5 + 16 Combine like terms: 30.5 + 16 = 46.5 16 + 8x + x2 = 46.5 Factor a perfect square on the left side: (x + 4)(x + 4) = 46.5 Calculate the square root of the right side: 6.819090848 Break this problem into two subproblems by setting (x + 4) equal to 6.819090848 and -6.819090848.Subproblem 1
x + 4 = 6.819090848 Simplifying x + 4 = 6.819090848 Reorder the terms: 4 + x = 6.819090848 Solving 4 + x = 6.819090848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 6.819090848 + -4 Combine like terms: 4 + -4 = 0 0 + x = 6.819090848 + -4 x = 6.819090848 + -4 Combine like terms: 6.819090848 + -4 = 2.819090848 x = 2.819090848 Simplifying x = 2.819090848Subproblem 2
x + 4 = -6.819090848 Simplifying x + 4 = -6.819090848 Reorder the terms: 4 + x = -6.819090848 Solving 4 + x = -6.819090848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -6.819090848 + -4 Combine like terms: 4 + -4 = 0 0 + x = -6.819090848 + -4 x = -6.819090848 + -4 Combine like terms: -6.819090848 + -4 = -10.819090848 x = -10.819090848 Simplifying x = -10.819090848Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.819090848, -10.819090848}
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