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Simplifying -19x2 + 76x = -4 Reorder the terms: 76x + -19x2 = -4 Solving 76x + -19x2 = -4 Solving for variable 'x'. Reorder the terms: 4 + 76x + -19x2 = -4 + 4 Combine like terms: -4 + 4 = 0 4 + 76x + -19x2 = 0 Begin completing the square. Divide all terms by -19 the coefficient of the squared term: Divide each side by '-19'. -0.2105263158 + -4x + x2 = 0 Move the constant term to the right: Add '0.2105263158' to each side of the equation. -0.2105263158 + -4x + 0.2105263158 + x2 = 0 + 0.2105263158 Reorder the terms: -0.2105263158 + 0.2105263158 + -4x + x2 = 0 + 0.2105263158 Combine like terms: -0.2105263158 + 0.2105263158 = 0.0000000000 0.0000000000 + -4x + x2 = 0 + 0.2105263158 -4x + x2 = 0 + 0.2105263158 Combine like terms: 0 + 0.2105263158 = 0.2105263158 -4x + x2 = 0.2105263158 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 0.2105263158 + 4 Reorder the terms: 4 + -4x + x2 = 0.2105263158 + 4 Combine like terms: 0.2105263158 + 4 = 4.2105263158 4 + -4x + x2 = 4.2105263158 Factor a perfect square on the left side: (x + -2)(x + -2) = 4.2105263158 Calculate the square root of the right side: 2.051956704 Break this problem into two subproblems by setting (x + -2) equal to 2.051956704 and -2.051956704.Subproblem 1
x + -2 = 2.051956704 Simplifying x + -2 = 2.051956704 Reorder the terms: -2 + x = 2.051956704 Solving -2 + x = 2.051956704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.051956704 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.051956704 + 2 x = 2.051956704 + 2 Combine like terms: 2.051956704 + 2 = 4.051956704 x = 4.051956704 Simplifying x = 4.051956704Subproblem 2
x + -2 = -2.051956704 Simplifying x + -2 = -2.051956704 Reorder the terms: -2 + x = -2.051956704 Solving -2 + x = -2.051956704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.051956704 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.051956704 + 2 x = -2.051956704 + 2 Combine like terms: -2.051956704 + 2 = -0.051956704 x = -0.051956704 Simplifying x = -0.051956704Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.051956704, -0.051956704}
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