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Simplifying 2.24x + -1(0.089x2) = 1 Remove parenthesis around (0.089x2) 2.24x + -1 * 0.089x2 = 1 Multiply -1 * 0.089 2.24x + -0.089x2 = 1 Solving 2.24x + -0.089x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + 2.24x + -0.089x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 2.24x + -0.089x2 = 0 Begin completing the square. Divide all terms by -0.089 the coefficient of the squared term: Divide each side by '-0.089'. 11.23595506 + -25.16853933x + x2 = 0 Move the constant term to the right: Add '-11.23595506' to each side of the equation. 11.23595506 + -25.16853933x + -11.23595506 + x2 = 0 + -11.23595506 Reorder the terms: 11.23595506 + -11.23595506 + -25.16853933x + x2 = 0 + -11.23595506 Combine like terms: 11.23595506 + -11.23595506 = 0.00000000 0.00000000 + -25.16853933x + x2 = 0 + -11.23595506 -25.16853933x + x2 = 0 + -11.23595506 Combine like terms: 0 + -11.23595506 = -11.23595506 -25.16853933x + x2 = -11.23595506 The x term is -25.16853933x. Take half its coefficient (-12.58426967). Square it (158.3638431) and add it to both sides. Add '158.3638431' to each side of the equation. -25.16853933x + 158.3638431 + x2 = -11.23595506 + 158.3638431 Reorder the terms: 158.3638431 + -25.16853933x + x2 = -11.23595506 + 158.3638431 Combine like terms: -11.23595506 + 158.3638431 = 147.12788804 158.3638431 + -25.16853933x + x2 = 147.12788804 Factor a perfect square on the left side: (x + -12.58426967)(x + -12.58426967) = 147.12788804 Calculate the square root of the right side: 12.12962852 Break this problem into two subproblems by setting (x + -12.58426967) equal to 12.12962852 and -12.12962852.Subproblem 1
x + -12.58426967 = 12.12962852 Simplifying x + -12.58426967 = 12.12962852 Reorder the terms: -12.58426967 + x = 12.12962852 Solving -12.58426967 + x = 12.12962852 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.58426967' to each side of the equation. -12.58426967 + 12.58426967 + x = 12.12962852 + 12.58426967 Combine like terms: -12.58426967 + 12.58426967 = 0.00000000 0.00000000 + x = 12.12962852 + 12.58426967 x = 12.12962852 + 12.58426967 Combine like terms: 12.12962852 + 12.58426967 = 24.71389819 x = 24.71389819 Simplifying x = 24.71389819Subproblem 2
x + -12.58426967 = -12.12962852 Simplifying x + -12.58426967 = -12.12962852 Reorder the terms: -12.58426967 + x = -12.12962852 Solving -12.58426967 + x = -12.12962852 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.58426967' to each side of the equation. -12.58426967 + 12.58426967 + x = -12.12962852 + 12.58426967 Combine like terms: -12.58426967 + 12.58426967 = 0.00000000 0.00000000 + x = -12.12962852 + 12.58426967 x = -12.12962852 + 12.58426967 Combine like terms: -12.12962852 + 12.58426967 = 0.45464115 x = 0.45464115 Simplifying x = 0.45464115Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.71389819, 0.45464115}
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