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Simplifying 16x2 + 19x + -36 = 0 Reorder the terms: -36 + 19x + 16x2 = 0 Solving -36 + 19x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -2.25 + 1.1875x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 1.1875x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 1.1875x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 1.1875x + x2 = 0 + 2.25 1.1875x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 1.1875x + x2 = 2.25 The x term is 1.1875x. Take half its coefficient (0.59375). Square it (0.3525390625) and add it to both sides. Add '0.3525390625' to each side of the equation. 1.1875x + 0.3525390625 + x2 = 2.25 + 0.3525390625 Reorder the terms: 0.3525390625 + 1.1875x + x2 = 2.25 + 0.3525390625 Combine like terms: 2.25 + 0.3525390625 = 2.6025390625 0.3525390625 + 1.1875x + x2 = 2.6025390625 Factor a perfect square on the left side: (x + 0.59375)(x + 0.59375) = 2.6025390625 Calculate the square root of the right side: 1.613238687 Break this problem into two subproblems by setting (x + 0.59375) equal to 1.613238687 and -1.613238687.Subproblem 1
x + 0.59375 = 1.613238687 Simplifying x + 0.59375 = 1.613238687 Reorder the terms: 0.59375 + x = 1.613238687 Solving 0.59375 + x = 1.613238687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.59375' to each side of the equation. 0.59375 + -0.59375 + x = 1.613238687 + -0.59375 Combine like terms: 0.59375 + -0.59375 = 0.00000 0.00000 + x = 1.613238687 + -0.59375 x = 1.613238687 + -0.59375 Combine like terms: 1.613238687 + -0.59375 = 1.019488687 x = 1.019488687 Simplifying x = 1.019488687Subproblem 2
x + 0.59375 = -1.613238687 Simplifying x + 0.59375 = -1.613238687 Reorder the terms: 0.59375 + x = -1.613238687 Solving 0.59375 + x = -1.613238687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.59375' to each side of the equation. 0.59375 + -0.59375 + x = -1.613238687 + -0.59375 Combine like terms: 0.59375 + -0.59375 = 0.00000 0.00000 + x = -1.613238687 + -0.59375 x = -1.613238687 + -0.59375 Combine like terms: -1.613238687 + -0.59375 = -2.206988687 x = -2.206988687 Simplifying x = -2.206988687Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.019488687, -2.206988687}
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