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Simplifying 5x2 + 23x + -35 = 0 Reorder the terms: -35 + 23x + 5x2 = 0 Solving -35 + 23x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7 + 4.6x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 4.6x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 4.6x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 4.6x + x2 = 0 + 7 4.6x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 4.6x + x2 = 7 The x term is 4.6x. Take half its coefficient (2.3). Square it (5.29) and add it to both sides. Add '5.29' to each side of the equation. 4.6x + 5.29 + x2 = 7 + 5.29 Reorder the terms: 5.29 + 4.6x + x2 = 7 + 5.29 Combine like terms: 7 + 5.29 = 12.29 5.29 + 4.6x + x2 = 12.29 Factor a perfect square on the left side: (x + 2.3)(x + 2.3) = 12.29 Calculate the square root of the right side: 3.505709629 Break this problem into two subproblems by setting (x + 2.3) equal to 3.505709629 and -3.505709629.Subproblem 1
x + 2.3 = 3.505709629 Simplifying x + 2.3 = 3.505709629 Reorder the terms: 2.3 + x = 3.505709629 Solving 2.3 + x = 3.505709629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.3' to each side of the equation. 2.3 + -2.3 + x = 3.505709629 + -2.3 Combine like terms: 2.3 + -2.3 = 0.0 0.0 + x = 3.505709629 + -2.3 x = 3.505709629 + -2.3 Combine like terms: 3.505709629 + -2.3 = 1.205709629 x = 1.205709629 Simplifying x = 1.205709629Subproblem 2
x + 2.3 = -3.505709629 Simplifying x + 2.3 = -3.505709629 Reorder the terms: 2.3 + x = -3.505709629 Solving 2.3 + x = -3.505709629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.3' to each side of the equation. 2.3 + -2.3 + x = -3.505709629 + -2.3 Combine like terms: 2.3 + -2.3 = 0.0 0.0 + x = -3.505709629 + -2.3 x = -3.505709629 + -2.3 Combine like terms: -3.505709629 + -2.3 = -5.805709629 x = -5.805709629 Simplifying x = -5.805709629Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.205709629, -5.805709629}
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