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Simplifying 1.63x2 + 3.21x + -7.24 = 0 Reorder the terms: -7.24 + 3.21x + 1.63x2 = 0 Solving -7.24 + 3.21x + 1.63x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.63 the coefficient of the squared term: Divide each side by '1.63'. -4.441717791 + 1.969325153x + x2 = 0 Move the constant term to the right: Add '4.441717791' to each side of the equation. -4.441717791 + 1.969325153x + 4.441717791 + x2 = 0 + 4.441717791 Reorder the terms: -4.441717791 + 4.441717791 + 1.969325153x + x2 = 0 + 4.441717791 Combine like terms: -4.441717791 + 4.441717791 = 0.000000000 0.000000000 + 1.969325153x + x2 = 0 + 4.441717791 1.969325153x + x2 = 0 + 4.441717791 Combine like terms: 0 + 4.441717791 = 4.441717791 1.969325153x + x2 = 4.441717791 The x term is 1.969325153x. Take half its coefficient (0.9846625765). Square it (0.9695603896) and add it to both sides. Add '0.9695603896' to each side of the equation. 1.969325153x + 0.9695603896 + x2 = 4.441717791 + 0.9695603896 Reorder the terms: 0.9695603896 + 1.969325153x + x2 = 4.441717791 + 0.9695603896 Combine like terms: 4.441717791 + 0.9695603896 = 5.4112781806 0.9695603896 + 1.969325153x + x2 = 5.4112781806 Factor a perfect square on the left side: (x + 0.9846625765)(x + 0.9846625765) = 5.4112781806 Calculate the square root of the right side: 2.32621542 Break this problem into two subproblems by setting (x + 0.9846625765) equal to 2.32621542 and -2.32621542.Subproblem 1
x + 0.9846625765 = 2.32621542 Simplifying x + 0.9846625765 = 2.32621542 Reorder the terms: 0.9846625765 + x = 2.32621542 Solving 0.9846625765 + x = 2.32621542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9846625765' to each side of the equation. 0.9846625765 + -0.9846625765 + x = 2.32621542 + -0.9846625765 Combine like terms: 0.9846625765 + -0.9846625765 = 0.0000000000 0.0000000000 + x = 2.32621542 + -0.9846625765 x = 2.32621542 + -0.9846625765 Combine like terms: 2.32621542 + -0.9846625765 = 1.3415528435 x = 1.3415528435 Simplifying x = 1.3415528435Subproblem 2
x + 0.9846625765 = -2.32621542 Simplifying x + 0.9846625765 = -2.32621542 Reorder the terms: 0.9846625765 + x = -2.32621542 Solving 0.9846625765 + x = -2.32621542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9846625765' to each side of the equation. 0.9846625765 + -0.9846625765 + x = -2.32621542 + -0.9846625765 Combine like terms: 0.9846625765 + -0.9846625765 = 0.0000000000 0.0000000000 + x = -2.32621542 + -0.9846625765 x = -2.32621542 + -0.9846625765 Combine like terms: -2.32621542 + -0.9846625765 = -3.3108779965 x = -3.3108779965 Simplifying x = -3.3108779965Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3415528435, -3.3108779965}
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