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Simplifying 9.23x2 + -5.26x + -2.37 = 0 Reorder the terms: -2.37 + -5.26x + 9.23x2 = 0 Solving -2.37 + -5.26x + 9.23x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9.23 the coefficient of the squared term: Divide each side by '9.23'. -0.2567713976 + -0.5698808234x + x2 = 0 Move the constant term to the right: Add '0.2567713976' to each side of the equation. -0.2567713976 + -0.5698808234x + 0.2567713976 + x2 = 0 + 0.2567713976 Reorder the terms: -0.2567713976 + 0.2567713976 + -0.5698808234x + x2 = 0 + 0.2567713976 Combine like terms: -0.2567713976 + 0.2567713976 = 0.0000000000 0.0000000000 + -0.5698808234x + x2 = 0 + 0.2567713976 -0.5698808234x + x2 = 0 + 0.2567713976 Combine like terms: 0 + 0.2567713976 = 0.2567713976 -0.5698808234x + x2 = 0.2567713976 The x term is -0.5698808234x. Take half its coefficient (-0.2849404117). Square it (0.08119103822) and add it to both sides. Add '0.08119103822' to each side of the equation. -0.5698808234x + 0.08119103822 + x2 = 0.2567713976 + 0.08119103822 Reorder the terms: 0.08119103822 + -0.5698808234x + x2 = 0.2567713976 + 0.08119103822 Combine like terms: 0.2567713976 + 0.08119103822 = 0.33796243582 0.08119103822 + -0.5698808234x + x2 = 0.33796243582 Factor a perfect square on the left side: (x + -0.2849404117)(x + -0.2849404117) = 0.33796243582 Calculate the square root of the right side: 0.581345367 Break this problem into two subproblems by setting (x + -0.2849404117) equal to 0.581345367 and -0.581345367.Subproblem 1
x + -0.2849404117 = 0.581345367 Simplifying x + -0.2849404117 = 0.581345367 Reorder the terms: -0.2849404117 + x = 0.581345367 Solving -0.2849404117 + x = 0.581345367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2849404117' to each side of the equation. -0.2849404117 + 0.2849404117 + x = 0.581345367 + 0.2849404117 Combine like terms: -0.2849404117 + 0.2849404117 = 0.0000000000 0.0000000000 + x = 0.581345367 + 0.2849404117 x = 0.581345367 + 0.2849404117 Combine like terms: 0.581345367 + 0.2849404117 = 0.8662857787 x = 0.8662857787 Simplifying x = 0.8662857787Subproblem 2
x + -0.2849404117 = -0.581345367 Simplifying x + -0.2849404117 = -0.581345367 Reorder the terms: -0.2849404117 + x = -0.581345367 Solving -0.2849404117 + x = -0.581345367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2849404117' to each side of the equation. -0.2849404117 + 0.2849404117 + x = -0.581345367 + 0.2849404117 Combine like terms: -0.2849404117 + 0.2849404117 = 0.0000000000 0.0000000000 + x = -0.581345367 + 0.2849404117 x = -0.581345367 + 0.2849404117 Combine like terms: -0.581345367 + 0.2849404117 = -0.2964049553 x = -0.2964049553 Simplifying x = -0.2964049553Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8662857787, -0.2964049553}
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