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Simplifying 5x2 + 22x + 15 = 0 Reorder the terms: 15 + 22x + 5x2 = 0 Solving 15 + 22x + 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'. 3 + 4.4x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 4.4x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 4.4x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4.4x + x2 = 0 + -3 4.4x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 4.4x + x2 = -3 The x term is 4.4x. Take half its coefficient (2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. 4.4x + 4.84 + x2 = -3 + 4.84 Reorder the terms: 4.84 + 4.4x + x2 = -3 + 4.84 Combine like terms: -3 + 4.84 = 1.84 4.84 + 4.4x + x2 = 1.84 Factor a perfect square on the left side: (x + 2.2)(x + 2.2) = 1.84 Calculate the square root of the right side: 1.356465997 Break this problem into two subproblems by setting (x + 2.2) equal to 1.356465997 and -1.356465997.Subproblem 1
x + 2.2 = 1.356465997 Simplifying x + 2.2 = 1.356465997 Reorder the terms: 2.2 + x = 1.356465997 Solving 2.2 + x = 1.356465997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.2' to each side of the equation. 2.2 + -2.2 + x = 1.356465997 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + x = 1.356465997 + -2.2 x = 1.356465997 + -2.2 Combine like terms: 1.356465997 + -2.2 = -0.843534003 x = -0.843534003 Simplifying x = -0.843534003Subproblem 2
x + 2.2 = -1.356465997 Simplifying x + 2.2 = -1.356465997 Reorder the terms: 2.2 + x = -1.356465997 Solving 2.2 + x = -1.356465997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.2' to each side of the equation. 2.2 + -2.2 + x = -1.356465997 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + x = -1.356465997 + -2.2 x = -1.356465997 + -2.2 Combine like terms: -1.356465997 + -2.2 = -3.556465997 x = -3.556465997 Simplifying x = -3.556465997Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.843534003, -3.556465997}
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