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Simplifying (4x2 + -7x + -8) = 0 Reorder the terms: (-8 + -7x + 4x2) = 0 Remove parenthesis around (-8 + -7x + 4x2) -8 + -7x + 4x2 = 0 Solving -8 + -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'. -2 + -1.75x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -1.75x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -1.75x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1.75x + x2 = 0 + 2 -1.75x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1.75x + x2 = 2 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 = 2 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = 2 + 0.765625 Combine like terms: 2 + 0.765625 = 2.765625 0.765625 + -1.75x + x2 = 2.765625 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = 2.765625 Calculate the square root of the right side: 1.663016837 Break this problem into two subproblems by setting (x + -0.875) equal to 1.663016837 and -1.663016837.Subproblem 1
x + -0.875 = 1.663016837 Simplifying x + -0.875 = 1.663016837 Reorder the terms: -0.875 + x = 1.663016837 Solving -0.875 + x = 1.663016837 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 = 1.663016837 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 1.663016837 + 0.875 x = 1.663016837 + 0.875 Combine like terms: 1.663016837 + 0.875 = 2.538016837 x = 2.538016837 Simplifying x = 2.538016837Subproblem 2
x + -0.875 = -1.663016837 Simplifying x + -0.875 = -1.663016837 Reorder the terms: -0.875 + x = -1.663016837 Solving -0.875 + x = -1.663016837 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 = -1.663016837 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -1.663016837 + 0.875 x = -1.663016837 + 0.875 Combine like terms: -1.663016837 + 0.875 = -0.788016837 x = -0.788016837 Simplifying x = -0.788016837Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.538016837, -0.788016837}
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