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Simplifying 5x2 + 24x + 7 = 0 Reorder the terms: 7 + 24x + 5x2 = 0 Solving 7 + 24x + 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 + 4.8x + x2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + 4.8x + -1.4 + x2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + 4.8x + x2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + 4.8x + x2 = 0 + -1.4 4.8x + x2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 4.8x + x2 = -1.4 The x term is 4.8x. Take half its coefficient (2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. 4.8x + 5.76 + x2 = -1.4 + 5.76 Reorder the terms: 5.76 + 4.8x + x2 = -1.4 + 5.76 Combine like terms: -1.4 + 5.76 = 4.36 5.76 + 4.8x + x2 = 4.36 Factor a perfect square on the left side: (x + 2.4)(x + 2.4) = 4.36 Calculate the square root of the right side: 2.088061302 Break this problem into two subproblems by setting (x + 2.4) equal to 2.088061302 and -2.088061302.Subproblem 1
x + 2.4 = 2.088061302 Simplifying x + 2.4 = 2.088061302 Reorder the terms: 2.4 + x = 2.088061302 Solving 2.4 + x = 2.088061302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + x = 2.088061302 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = 2.088061302 + -2.4 x = 2.088061302 + -2.4 Combine like terms: 2.088061302 + -2.4 = -0.311938698 x = -0.311938698 Simplifying x = -0.311938698Subproblem 2
x + 2.4 = -2.088061302 Simplifying x + 2.4 = -2.088061302 Reorder the terms: 2.4 + x = -2.088061302 Solving 2.4 + x = -2.088061302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + x = -2.088061302 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = -2.088061302 + -2.4 x = -2.088061302 + -2.4 Combine like terms: -2.088061302 + -2.4 = -4.488061302 x = -4.488061302 Simplifying x = -4.488061302Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.311938698, -4.488061302}
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