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Simplifying 5x2 + 23x + -5 = 0 Reorder the terms: -5 + 23x + 5x2 = 0 Solving -5 + 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'. -1 + 4.6x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 4.6x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 4.6x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4.6x + x2 = 0 + 1 4.6x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 4.6x + x2 = 1 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 = 1 + 5.29 Reorder the terms: 5.29 + 4.6x + x2 = 1 + 5.29 Combine like terms: 1 + 5.29 = 6.29 5.29 + 4.6x + x2 = 6.29 Factor a perfect square on the left side: (x + 2.3)(x + 2.3) = 6.29 Calculate the square root of the right side: 2.507987241 Break this problem into two subproblems by setting (x + 2.3) equal to 2.507987241 and -2.507987241.Subproblem 1
x + 2.3 = 2.507987241 Simplifying x + 2.3 = 2.507987241 Reorder the terms: 2.3 + x = 2.507987241 Solving 2.3 + x = 2.507987241 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 = 2.507987241 + -2.3 Combine like terms: 2.3 + -2.3 = 0.0 0.0 + x = 2.507987241 + -2.3 x = 2.507987241 + -2.3 Combine like terms: 2.507987241 + -2.3 = 0.207987241 x = 0.207987241 Simplifying x = 0.207987241Subproblem 2
x + 2.3 = -2.507987241 Simplifying x + 2.3 = -2.507987241 Reorder the terms: 2.3 + x = -2.507987241 Solving 2.3 + x = -2.507987241 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 = -2.507987241 + -2.3 Combine like terms: 2.3 + -2.3 = 0.0 0.0 + x = -2.507987241 + -2.3 x = -2.507987241 + -2.3 Combine like terms: -2.507987241 + -2.3 = -4.807987241 x = -4.807987241 Simplifying x = -4.807987241Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.207987241, -4.807987241}
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