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Simplifying 7x2 + -21x + 10 = 0 Reorder the terms: 10 + -21x + 7x2 = 0 Solving 10 + -21x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.428571429 + -3x + x2 = 0 Move the constant term to the right: Add '-1.428571429' to each side of the equation. 1.428571429 + -3x + -1.428571429 + x2 = 0 + -1.428571429 Reorder the terms: 1.428571429 + -1.428571429 + -3x + x2 = 0 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + -3x + x2 = 0 + -1.428571429 -3x + x2 = 0 + -1.428571429 Combine like terms: 0 + -1.428571429 = -1.428571429 -3x + x2 = -1.428571429 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -1.428571429 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -1.428571429 + 2.25 Combine like terms: -1.428571429 + 2.25 = 0.821428571 2.25 + -3x + x2 = 0.821428571 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 0.821428571 Calculate the square root of the right side: 0.906326967 Break this problem into two subproblems by setting (x + -1.5) equal to 0.906326967 and -0.906326967.Subproblem 1
x + -1.5 = 0.906326967 Simplifying x + -1.5 = 0.906326967 Reorder the terms: -1.5 + x = 0.906326967 Solving -1.5 + x = 0.906326967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 0.906326967 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 0.906326967 + 1.5 x = 0.906326967 + 1.5 Combine like terms: 0.906326967 + 1.5 = 2.406326967 x = 2.406326967 Simplifying x = 2.406326967Subproblem 2
x + -1.5 = -0.906326967 Simplifying x + -1.5 = -0.906326967 Reorder the terms: -1.5 + x = -0.906326967 Solving -1.5 + x = -0.906326967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -0.906326967 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -0.906326967 + 1.5 x = -0.906326967 + 1.5 Combine like terms: -0.906326967 + 1.5 = 0.593673033 x = 0.593673033 Simplifying x = 0.593673033Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.406326967, 0.593673033}
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