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Simplifying 4(x * x) + -7x + -19 = 0 Multiply x * x 4(x2) + -7x + -19 = 0 Reorder the terms: -19 + -7x + 4x2 = 0 Solving -19 + -7x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.75 + -1.75x + x2 = 0 Move the constant term to the right: Add '4.75' to each side of the equation. -4.75 + -1.75x + 4.75 + x2 = 0 + 4.75 Reorder the terms: -4.75 + 4.75 + -1.75x + x2 = 0 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + -1.75x + x2 = 0 + 4.75 -1.75x + x2 = 0 + 4.75 Combine like terms: 0 + 4.75 = 4.75 -1.75x + x2 = 4.75 The x term is -1.75x. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75x + 0.765625 + x2 = 4.75 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = 4.75 + 0.765625 Combine like terms: 4.75 + 0.765625 = 5.515625 0.765625 + -1.75x + x2 = 5.515625 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = 5.515625 Calculate the square root of the right side: 2.348536779 Break this problem into two subproblems by setting (x + -0.875) equal to 2.348536779 and -2.348536779.Subproblem 1
x + -0.875 = 2.348536779 Simplifying x + -0.875 = 2.348536779 Reorder the terms: -0.875 + x = 2.348536779 Solving -0.875 + x = 2.348536779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = 2.348536779 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 2.348536779 + 0.875 x = 2.348536779 + 0.875 Combine like terms: 2.348536779 + 0.875 = 3.223536779 x = 3.223536779 Simplifying x = 3.223536779Subproblem 2
x + -0.875 = -2.348536779 Simplifying x + -0.875 = -2.348536779 Reorder the terms: -0.875 + x = -2.348536779 Solving -0.875 + x = -2.348536779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = -2.348536779 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -2.348536779 + 0.875 x = -2.348536779 + 0.875 Combine like terms: -2.348536779 + 0.875 = -1.473536779 x = -1.473536779 Simplifying x = -1.473536779Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.223536779, -1.473536779}
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