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Simplifying 4x2 + 28x = -5 Reorder the terms: 28x + 4x2 = -5 Solving 28x + 4x2 = -5 Solving for variable 'x'. Reorder the terms: 5 + 28x + 4x2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + 28x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 7x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 7x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 7x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 7x + x2 = 0 + -1.25 7x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 7x + x2 = -1.25 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 = -1.25 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -1.25 + 12.25 Combine like terms: -1.25 + 12.25 = 11 12.25 + 7x + x2 = 11 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + 3.5) equal to 3.31662479 and -3.31662479.Subproblem 1
x + 3.5 = 3.31662479 Simplifying x + 3.5 = 3.31662479 Reorder the terms: 3.5 + x = 3.31662479 Solving 3.5 + x = 3.31662479 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 = 3.31662479 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.31662479 + -3.5 x = 3.31662479 + -3.5 Combine like terms: 3.31662479 + -3.5 = -0.18337521 x = -0.18337521 Simplifying x = -0.18337521Subproblem 2
x + 3.5 = -3.31662479 Simplifying x + 3.5 = -3.31662479 Reorder the terms: 3.5 + x = -3.31662479 Solving 3.5 + x = -3.31662479 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 = -3.31662479 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.31662479 + -3.5 x = -3.31662479 + -3.5 Combine like terms: -3.31662479 + -3.5 = -6.81662479 x = -6.81662479 Simplifying x = -6.81662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.18337521, -6.81662479}
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