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Simplifying 5x2 + 23x + 23 = 0 Reorder the terms: 23 + 23x + 5x2 = 0 Solving 23 + 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'. 4.6 + 4.6x + x2 = 0 Move the constant term to the right: Add '-4.6' to each side of the equation. 4.6 + 4.6x + -4.6 + x2 = 0 + -4.6 Reorder the terms: 4.6 + -4.6 + 4.6x + x2 = 0 + -4.6 Combine like terms: 4.6 + -4.6 = 0.0 0.0 + 4.6x + x2 = 0 + -4.6 4.6x + x2 = 0 + -4.6 Combine like terms: 0 + -4.6 = -4.6 4.6x + x2 = -4.6 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 = -4.6 + 5.29 Reorder the terms: 5.29 + 4.6x + x2 = -4.6 + 5.29 Combine like terms: -4.6 + 5.29 = 0.69 5.29 + 4.6x + x2 = 0.69 Factor a perfect square on the left side: (x + 2.3)(x + 2.3) = 0.69 Calculate the square root of the right side: 0.830662386 Break this problem into two subproblems by setting (x + 2.3) equal to 0.830662386 and -0.830662386.Subproblem 1
x + 2.3 = 0.830662386 Simplifying x + 2.3 = 0.830662386 Reorder the terms: 2.3 + x = 0.830662386 Solving 2.3 + x = 0.830662386 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 = 0.830662386 + -2.3 Combine like terms: 2.3 + -2.3 = 0.0 0.0 + x = 0.830662386 + -2.3 x = 0.830662386 + -2.3 Combine like terms: 0.830662386 + -2.3 = -1.469337614 x = -1.469337614 Simplifying x = -1.469337614Subproblem 2
x + 2.3 = -0.830662386 Simplifying x + 2.3 = -0.830662386 Reorder the terms: 2.3 + x = -0.830662386 Solving 2.3 + x = -0.830662386 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 = -0.830662386 + -2.3 Combine like terms: 2.3 + -2.3 = 0.0 0.0 + x = -0.830662386 + -2.3 x = -0.830662386 + -2.3 Combine like terms: -0.830662386 + -2.3 = -3.130662386 x = -3.130662386 Simplifying x = -3.130662386Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.469337614, -3.130662386}
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