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Simplifying 7 + 26x + -40x2 = 0 Solving 7 + 26x + -40x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -40 the coefficient of the squared term: Divide each side by '-40'. -0.175 + -0.65x + x2 = 0 Move the constant term to the right: Add '0.175' to each side of the equation. -0.175 + -0.65x + 0.175 + x2 = 0 + 0.175 Reorder the terms: -0.175 + 0.175 + -0.65x + x2 = 0 + 0.175 Combine like terms: -0.175 + 0.175 = 0.000 0.000 + -0.65x + x2 = 0 + 0.175 -0.65x + x2 = 0 + 0.175 Combine like terms: 0 + 0.175 = 0.175 -0.65x + x2 = 0.175 The x term is -0.65x. Take half its coefficient (-0.325). Square it (0.105625) and add it to both sides. Add '0.105625' to each side of the equation. -0.65x + 0.105625 + x2 = 0.175 + 0.105625 Reorder the terms: 0.105625 + -0.65x + x2 = 0.175 + 0.105625 Combine like terms: 0.175 + 0.105625 = 0.280625 0.105625 + -0.65x + x2 = 0.280625 Factor a perfect square on the left side: (x + -0.325)(x + -0.325) = 0.280625 Calculate the square root of the right side: 0.529740503 Break this problem into two subproblems by setting (x + -0.325) equal to 0.529740503 and -0.529740503.Subproblem 1
x + -0.325 = 0.529740503 Simplifying x + -0.325 = 0.529740503 Reorder the terms: -0.325 + x = 0.529740503 Solving -0.325 + x = 0.529740503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.325' to each side of the equation. -0.325 + 0.325 + x = 0.529740503 + 0.325 Combine like terms: -0.325 + 0.325 = 0.000 0.000 + x = 0.529740503 + 0.325 x = 0.529740503 + 0.325 Combine like terms: 0.529740503 + 0.325 = 0.854740503 x = 0.854740503 Simplifying x = 0.854740503Subproblem 2
x + -0.325 = -0.529740503 Simplifying x + -0.325 = -0.529740503 Reorder the terms: -0.325 + x = -0.529740503 Solving -0.325 + x = -0.529740503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.325' to each side of the equation. -0.325 + 0.325 + x = -0.529740503 + 0.325 Combine like terms: -0.325 + 0.325 = 0.000 0.000 + x = -0.529740503 + 0.325 x = -0.529740503 + 0.325 Combine like terms: -0.529740503 + 0.325 = -0.204740503 x = -0.204740503 Simplifying x = -0.204740503Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.854740503, -0.204740503}
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