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Simplifying 4x2 + 28x + 9 = 0 Reorder the terms: 9 + 28x + 4x2 = 0 Solving 9 + 28x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + 7x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 7x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 7x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 7x + x2 = 0 + -2.25 7x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 7x + x2 = -2.25 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -2.25 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -2.25 + 12.25 Combine like terms: -2.25 + 12.25 = 10 12.25 + 7x + x2 = 10 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + 3.5) equal to 3.16227766 and -3.16227766.Subproblem 1
x + 3.5 = 3.16227766 Simplifying x + 3.5 = 3.16227766 Reorder the terms: 3.5 + x = 3.16227766 Solving 3.5 + x = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 3.16227766 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.16227766 + -3.5 x = 3.16227766 + -3.5 Combine like terms: 3.16227766 + -3.5 = -0.33772234 x = -0.33772234 Simplifying x = -0.33772234Subproblem 2
x + 3.5 = -3.16227766 Simplifying x + 3.5 = -3.16227766 Reorder the terms: 3.5 + x = -3.16227766 Solving 3.5 + x = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -3.16227766 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.16227766 + -3.5 x = -3.16227766 + -3.5 Combine like terms: -3.16227766 + -3.5 = -6.66227766 x = -6.66227766 Simplifying x = -6.66227766Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.33772234, -6.66227766}
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