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Simplifying 4x2 + 22x + -15 = 0 Reorder the terms: -15 + 22x + 4x2 = 0 Solving -15 + 22x + 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'. -3.75 + 5.5x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 5.5x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 5.5x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 5.5x + x2 = 0 + 3.75 5.5x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 5.5x + x2 = 3.75 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = 3.75 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 3.75 + 7.5625 Combine like terms: 3.75 + 7.5625 = 11.3125 7.5625 + 5.5x + x2 = 11.3125 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 11.3125 Calculate the square root of the right side: 3.363406012 Break this problem into two subproblems by setting (x + 2.75) equal to 3.363406012 and -3.363406012.Subproblem 1
x + 2.75 = 3.363406012 Simplifying x + 2.75 = 3.363406012 Reorder the terms: 2.75 + x = 3.363406012 Solving 2.75 + x = 3.363406012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 3.363406012 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 3.363406012 + -2.75 x = 3.363406012 + -2.75 Combine like terms: 3.363406012 + -2.75 = 0.613406012 x = 0.613406012 Simplifying x = 0.613406012Subproblem 2
x + 2.75 = -3.363406012 Simplifying x + 2.75 = -3.363406012 Reorder the terms: 2.75 + x = -3.363406012 Solving 2.75 + x = -3.363406012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -3.363406012 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -3.363406012 + -2.75 x = -3.363406012 + -2.75 Combine like terms: -3.363406012 + -2.75 = -6.113406012 x = -6.113406012 Simplifying x = -6.113406012Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.613406012, -6.113406012}
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