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Simplifying 4x2 + 20x + -11 = 4 Reorder the terms: -11 + 20x + 4x2 = 4 Solving -11 + 20x + 4x2 = 4 Solving for variable 'x'. Reorder the terms: -11 + -4 + 20x + 4x2 = 4 + -4 Combine like terms: -11 + -4 = -15 -15 + 20x + 4x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -15 + 20x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + 5x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 5x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 5x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 5x + x2 = 0 + 3.75 5x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 5x + x2 = 3.75 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 3.75 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 3.75 + 6.25 Combine like terms: 3.75 + 6.25 = 10 6.25 + 5x + x2 = 10 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + 2.5) equal to 3.16227766 and -3.16227766.Subproblem 1
x + 2.5 = 3.16227766 Simplifying x + 2.5 = 3.16227766 Reorder the terms: 2.5 + x = 3.16227766 Solving 2.5 + x = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 3.16227766 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.16227766 + -2.5 x = 3.16227766 + -2.5 Combine like terms: 3.16227766 + -2.5 = 0.66227766 x = 0.66227766 Simplifying x = 0.66227766Subproblem 2
x + 2.5 = -3.16227766 Simplifying x + 2.5 = -3.16227766 Reorder the terms: 2.5 + x = -3.16227766 Solving 2.5 + x = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -3.16227766 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.16227766 + -2.5 x = -3.16227766 + -2.5 Combine like terms: -3.16227766 + -2.5 = -5.66227766 x = -5.66227766 Simplifying x = -5.66227766Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.66227766, -5.66227766}
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