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Simplifying 0 = -7x2 + 7x + 4 Reorder the terms: 0 = 4 + 7x + -7x2 Solving 0 = 4 + 7x + -7x2 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + -7x + 7x2 = 4 + 7x + -7x2 + -4 + -7x + 7x2 Reorder the terms: -4 + -7x + 7x2 = 4 + -4 + 7x + -7x + -7x2 + 7x2 Combine like terms: 4 + -4 = 0 -4 + -7x + 7x2 = 0 + 7x + -7x + -7x2 + 7x2 -4 + -7x + 7x2 = 7x + -7x + -7x2 + 7x2 Combine like terms: 7x + -7x = 0 -4 + -7x + 7x2 = 0 + -7x2 + 7x2 -4 + -7x + 7x2 = -7x2 + 7x2 Combine like terms: -7x2 + 7x2 = 0 -4 + -7x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.5714285714 + -1x + x2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + -1x + 0.5714285714 + x2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + -1x + x2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + -1x + x2 = 0 + 0.5714285714 -1x + x2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 -1x + x2 = 0.5714285714 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.5714285714 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.5714285714 + 0.25 Combine like terms: 0.5714285714 + 0.25 = 0.8214285714 0.25 + -1x + x2 = 0.8214285714 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.8214285714 Calculate the square root of the right side: 0.906326967 Break this problem into two subproblems by setting (x + -0.5) equal to 0.906326967 and -0.906326967.Subproblem 1
x + -0.5 = 0.906326967 Simplifying x + -0.5 = 0.906326967 Reorder the terms: -0.5 + x = 0.906326967 Solving -0.5 + x = 0.906326967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.906326967 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.906326967 + 0.5 x = 0.906326967 + 0.5 Combine like terms: 0.906326967 + 0.5 = 1.406326967 x = 1.406326967 Simplifying x = 1.406326967Subproblem 2
x + -0.5 = -0.906326967 Simplifying x + -0.5 = -0.906326967 Reorder the terms: -0.5 + x = -0.906326967 Solving -0.5 + x = -0.906326967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.906326967 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.906326967 + 0.5 x = -0.906326967 + 0.5 Combine like terms: -0.906326967 + 0.5 = -0.406326967 x = -0.406326967 Simplifying x = -0.406326967Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.406326967, -0.406326967}
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